Trắc nghiệm hình tọa độ không gian có lời giải chi tiết, Exercises of Mathematics

Download Trắc nghiệm hình tọa độ không gian có lời giải chi tiết and more Exercises Mathematics in PDF only on Docsity! Nh6m Dé file word Chuyén dé Oxyz CHUYEN DE HiNH HOC TOA DO TRONG KHONG GIAN Cau 1. Trong khéng gian Oxyz voi hé toa dé (0; i i) cho OA =-i+3k.Tim toa do diém A A. (-1;0;3) B. (0;-1;3) C. (-1;3;0) D. (-1;3) Cau 2. Trong khéng gian Oxyz, cho diém M(-1;2;3) . Toa d6 hinh chiéu cia M trén truc Ox la: A. (-1,2; 0) B. (-1,0; 0) Cc. (0;0; 3) D. (0; 2;0) Cau 3. Trong khéng gian Oxyz, cho vecto OM =i- V3j+ Ak. Goi M’ 1a hinh chiéu vudng gdc cia M trén mp(Oxy). Khi dé toa dé ctia diém M’ trong hé toa dé Oxyz 1a A. (1;-v3;4) B. (1:4;-V3) Cc. (0;0; 4) D. (1; 4;0) Cau 4. Cho ba diém A(3,1,0); B(2,1,-1); C(x,y,-1). Tinh x,y dé (2-4-3) la trong tam tam gidc ABC A. x=2, y=1 B. x=2, y=-1 C. x=-2, y=-1 D. x=1, y=-5 Cau5. Trong khéng gian Oxyz, cho hinh binh hanh ABCD, biét A(1,0,0); B(0,0,1); C(2,1,1). Toa dé diém D 1a: A. (3,1,0) B. (3;-1;0) C. (-31;0) D. (1;3;0) Cau 6. Cho ba diém A(2,-1,1); B (3,-2, -1) . Tim diém N trén x’Ox cach déu A va B. A. (4;0;0) B. (-4;0;0) C. (1;4;0) D. (2;0;4) Cau7. Trong khéng gian Oxyz, diém M nam trén mat phang(Oxy), cach déu ba diém A (2, -3,1),B(0; 4 3),C(-3; 2; 2) c6 toa dé la: A. [Zo] B. (-3;-6;7) C. (-1;-13;14) D. era) 25° 50 7 14 Cau 8. (De chuyén - Thai Binh — lan 3) Trong khéng gian véi hé toa dé Oxyz, cho A(2; 0; 0), B(0; 3; 1), C(-3; 6; 4). Goi M 1a diém nam trén doan BC sao cho MC = 2MB Dé dai doan AM 1a: A. 27 B. ¥29 C. 3 D. ¥30 Cau9. Trong khéng gian Oxyz, cho ba diém A(2;-1;1), B(-1,3;-1) va C(5,-3;4). Tinh tich vé hung hai vecto ABBC. A. ABBC =48. B. ABBC =-48. C. ABBC =52. D. ABBC =-52. Cau 10. Trong khéng gian Oxyz, cho hai diém M(-1;5;-3), N(7;—-2;—-5) . Tinh dé dai doan MN. A, MN =V13. B, MN =3v13, c, MN=¥109 | Dp. MN=213. Cau ll. Trong khéng gian Oxyz, cho tam gidc ABC cé toa dé cdc dinh A(-4;9;-9), B(2;12;-2) va C(-m—2;,1—m;m+5) . Tim m dé tam gidc ABC vuéng tai B. A, m=3. B, m=-3. Cc, m=4. D, m=-4. Cau 12. Trong khéng gian Oxyz, cho tam gidc ABC cé toa dé cac dinh A(4;2;3), B(1;-2;-9) va C(-1,2; 2) . Xac dinh gid tri z dé tam gidc ABC cn tai A. g=-15 z=15 z=15 g=-15 A. B. Cc. D. z=9 z=-9 z=9 z=-9 Trang 1 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 13. Trong khéng gian Oxyz, cho tam gidc ABC vuéng can tai C va cé caéc dinh A €(Oxz), B(-2;3;1) va C(-1;1;-1). Tim toa d6 diém A. A. A(1,0;-1). B. A(-1,0;1). Cc. A(-1;0;-1). D. A(140;1). Cau 14. Trong khéng gian Oxyz, cho tam gidc ABC cé toa dé cac dinh A(2;1;-1), B(;3;1) va C(3;1;4) . Xac dinh toa d6 diém H 1a chan dudng cao xuat phat tir dinh B cia tam gidc ABC. A. Het 12%) B. He 1) Cc. Ht, By D. HS, 26 = =26 26 26 26 26 26 Cau 15. (Trich $6 GD&DT Binh Thuan). Trong khong gian voi hé truc toa d6 Oxyz, cho hai vecto w= (-3; 1,6) va v= (-1; -1;3) . Tim toa d6 cia vevto [uv] : A. [470 ]= (93:4) B. [130 ]=(9;-3:4) Cc. [4:2 |= (-9:3:4) D. [4:0 |=(9:3;-4) Cau 16. (THPT Kim Lién Ha NGi) Trong khong gian voi hé toa d6 Oxyz,cho ba diém A (2;-1;3), B (4 0;1) va C(-10; 5;3). Vecto nao didi day 1a vecto phap tuyén ctia mat phang (ABC)? _ _ _ A. n,(1;2;0). B. n, (1;2;2). C. n, (1; 8,2). D. n, (1;-2;2). Cau 17. Trong khéng gian voi hé toa dd Oxyz, cho 3 vectoa= (1;2;1),b = (-1;1;2),¢ = (x; 3x;x+2) : 19 -S 26) Ba vecto a,b,c dong phang khi: A. x=-2 B. x=1 C.x=2 D. x=-1 Cau 18. Cho tt dién ABCD biét A(0;0;1),B(2;3;5),C(6; 2;3),D(3;7;2). Thé tich cha tte dién ABCD bang A. 10 B. 20 c. 30 D. 40 Cau 19. Trong khéng gian vdi hé toa dd Oxyz,cho tam giac ABC cd A(2;—1;—2),B(—1;1;2), C(—1;1;0). Tinh dé dai dudng cao xuat phat tr A? a8 B. 2v13, c. Vis D. v3 2 2 Cau 20. Trong khéng gian voi hé toa dd Oxyz, cho 3 diém A (3 3;0),B (3 0;3),C (0;3;3) . Tim toa dé tam dung tron ngoai tiép tam gidc ABC. A. (2;-1;2) B. (2;2;1) C. (2;2;2) D. (-1;2;2) Cau 21. Trong khéng gian Oxyz cho ba vector a, b va é khac 0. Khang dinh nao sai? A. i cung phuong b =[7,b |=0. B. a, b, é déng phang =| i,b ]é=0. C. a,b, 7 khong ding phing @[4,5]é+0 D. a i, @|.cos(a,b}. Cau 22. Trong khéng gian véi hé toa dé Oxyz, cho tam gidc ABC cd A(1;0;0), B(0;0;1), C(2;1;1) . Dién tich cha tam giac ABC bang: a. 38. o . p ZH 2 2 2 2 Cau 23. Trong khéng gian véi hé toa dé Oxyz, cho tte dién ABCD véi A(1;0;0), B(0;1;0), C(0;0;1), D(-2;1;-1). Thé tich cia ti dién ABCD bang: Al B.2 c. >. D. wle Trang 2 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 42. Trong khéng gian voi hé toa dé Oxyz, cho mat cau (S) di qua diém A (1 2;3), B (2; 0; -2) va cé tam nam trén truc Ox. Viét phuong trinh ctia mat cau (S). A. (xt) +(y+2) +27 =29. B. (x+3) +? +2 =29 C2 +y? +(24+3) =29 D. (x-3) +y? +2 =29. Cau 43. Trong khéng gian Oxyz,cho mat phang (P):2x+ y-2z+10=0 va diém 1(2; 1; 3). Phuong trinh mat cau (S) tam I c&t mat phang (P) theo mét didng tron (c) cé ban kinh bang Ala A. (x+-2) +(y+1) +(2+3) =25. B. (x2) +(y-1) +(z-3) =7 C. (x42) +(y-1) +(z-3) =9. D. (x-2) +(y-1) +(2-3) =25. Cau 44. (BE SO GD DT THAI BINH) Cho méat phing (o):4v-2y+3z+1=0 va mat cu (S):x?+¥? +2°—2x+ 4y+ 6z = 0. Khi dé ménh dé nao sau day 14 ménh dé sai: A. (a) 06 diém chung véi (S). B. (a) ct (S) theo mét dudng tron. C. (@) tiép xtc véi (S).D. (@) di qua tam cia (S). Cau 45. (S6 GD&DT Ha Ni) Trong khéng gian Oxyz, cho diém uf p>0) va mat cau (S):a7 + y +2 =8. Dudng thang d thay déi, di qua diém M, cat mat cau (s) tai hai diém A,B phan biét. Tinh dién tich lén nhat $ ctia tam gidc OAB . A. S=y7. B. S=4. Cc. S=27. D. $=2y2. Cau 46. (THPT Hai Ba Trung Lan 2 - Hué 2017) Trong khéng gian Oxyz, cho mat cau (S):(x-1) +(y +3)" +(z-2) =49 va diém M(7;-1,5). Phuong trinh mat phang tip xuic voi mat cau (S) tai diém M 1a: A. x+2y+2z-15=0. B. 6x-2y—2z-34=0.C. 6x+2y+ 3z-55=0.D. 7x-y+5z-55=0. Cau 47. (THPT Chuyén DHSP Ha Noi Lan 3 - 2017) Trong khéng gian voi hé toa dé Oxyz, cho hai diém A(0; -1,0), B(11;-1) va mat cau (S) ity +2? —2x+4y-22-3=0. Mat phang (P) di qua A, B va cAt mat cau (S) theo giao tuyén 1a dudng tron cé ban kinh lén nhat cé phuong trinh 1a A. x-2y+3z-2=0. B. x-2y-3z-2=0. C. x+2y-3z-6=0. D. 2x-y-1=0. Cau 48. (THPT Chuyén Lam Son Thanh Hoa - 2017) Trong khong gian voi hé toa d6 Oxyz, cho diém 1(2; 41) va mat phang (P) :x+y+z—4=0. Tim phuong trinh mat cau (S) cé tam I sao cho (S) cAt mat phang (P) theo m6t durong tron cé duong kinh bang 2. A. (x42) +(yt4) +(z41) =4. B. (x-2) +(y-4) +(z-1) =4. C. (x-2) +(y-4y +(z-1) =3. D. (x-1) +(y+2) +(z-4) =3. Cau 49. (S6 GD&DT Thanh Hoa - 2017) Trong khéng gian voi hé toa dé Oxyz, cho duong x-2 y-1 z+1 So va diém 1(2;-1;1). Viét phuong trinh mat cau cé tam I va cat duong thang d tai hai diém A,B sao cho tam gidc IAB vudng tai I. thang, d: Trang 5 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz A. (x-2) +(y+1) +(2-1) =8. B. (x-2)'+(y+1) +(z-1) -2. C. (x-2)'+(ytl) +(z-1) =9. D. (x+2)'+(y-1) +(z+1) =9. Cau 50. (THPT Ha Huy Tap Lan 1 - Ha Tinh - 2017) Trong khéng gian Oxyz, cho diém M(2;1,1), mat phang(a):x+y+z-4=0 va mat cau (S):x° +? + 2? - 6x- 6y-8z+18=0. Phuong trinh duong thang A di qua M va nam trong (a) cat mat cau (s) theo mét doan thang cé 46 dai nhé nhat 1a: A. x-2_ y-1_z-1p x=2_ y-1_ z-1 c x=2_ y-1_z-1 py x-2_ y-1_ 2-1 -2 1 1 1 -2 1 1 2 -3 1 1 -2 Cau 51. Trong khéng gian voi hé toa dd Oxyz, cho mat cau (S):(x-5) +(y+4y +27 =9. Hay fim toa dé tam I va bankinh R ctia mat cau (S)? A. 1(5;4;0),R=3. — B. I(-5;4;0),R=9. C. 1(5;-4;0),R=9. D. 1(5;-4;0),R=3. Cau 52. ( DE THI THU NGHIEM BGD 2017) Trong khéng gian voi hé toa d6 Oxyz, phuong trinh nao dui day 1a phuong trinh cua mat cau cé tam 1(1;2; -1) va tiép xuc voi mat phang (P):x-2y-2z-8 =0? A. (x41) +(y+2) +(2-1) =3. B. (x-1)' +(y-2) +(z+1) =3. C. (x=1) +(y-2) +(z+1) =9. D. (x+1) +(y+2) +(z-1) =9. Cau 53. Mat cau di qua bén diém A (6;-2;3),B(0;1;6),C(2;0;-1),D(4;1;0) cé phuong trinh la: A. +y +27 4+4x-2y+6z-3=0. B. 2° +? +2°-4x+2y-6z-3=0. Cty +2? — 4x4 2y-6z-3=0. D. x+y? +2°- 4x4 2y-6z4+3=0. Cau 54. Trong khong gian voi hé toa dé Oxyz, cho diém A(2; -1;0) va mat phang (P):x-2y+z+2= 0.Goi I 1a hinh chiéu vudéng géc cua A trén mat phang (P). Phuong trinh mat c4u di qua A vacé tam I la: A. (x1) +(y+1) +(z41) =6. B. (x+1) +(y-1) +(z+1) =6. C. (x1) +(y-1) +(z41)° =6. D. (x+1) +(y+1) +(z-1) =6. x=t Cau 55. Cho d:;y=-l va 2 mat phang (a):x+2y+2z+3=0;(B):x+2y+2z+7 =0.Viet Z=-t phuong trinh mat cau cé tam I thuéc dung thang d va tiép xtic voi hai mat phang (z),(B)- A. (-3) (y+) +(243) = 5, B.xte(y-tp +2 5. 4 4 Cc. M4(ytl) t2*= 5. D. (x43) Hy tI) +(2-3)'=5. Cau 56. Trong khéng gian véi hé toa dé Oxyz cho ba diém A(a;0;0),B(0;b;0),C(0;0;c) voi a,b,c la cdc s6 thizc duong thay déi thoa man 24 2o1, Ki hiéu (S) Ja mat cau cé tam 1a a c gdc toa dd O, tiép xc vi mat phang (ABC) . Tim ban kinh lén nhat cua (5). AL3. B. V5. C. 25. D. 9. Trang 6 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 57. (NB) Trong khéng gian voi hé truc toa dd Oxyz, phuong trinh mat cau (S) cé tam 1(1;2;3) , ban kinh r= 2 c6é phuong trinh 1a: A. (x-1)' +(y-2) +(z-3) =2. B, (x41) +(y+2) +(24+3) =4. C. (x+1)'-(y+2) -(243) =4. D. (x-1) +(y-2)' + (2-3) =4. Cau 58. (NB) Trong khéng gian vi hé truc toa d6 Oxyz, xac dinh toa dé tam I va ban kinhr cua mat cau (S).x° + y?+ 2? -2x+6y-8z+1=0 A. I(1-3;4);r=5. B. I(-1;3;-4);r =5 C. 1(1;-3;4);r = 25 D. I(1;-3;4);r=-5. Cau 59. (TH) Trong khong gian voi hé truc toa d6 Oxyz, phurong trinh nao dudi day 14 phuong trinh cha mat cau cé tam I(-1;1;2) va tiép xtc voi mat phang (P):2x- y-3z-5=02 A. (x-1)'+(y+1) +(2+2) =V14. B. (x+1) +(y-1) +(z-2) =14. C. (x+1)'-(y-1) -(2-2) =14. D. (x+1)+(y-1)+(z-2)=14. Cau 60. (TH- Dé khao sat tinh Quang Ninh-2017) Trong khéng gian véi hé truc toa dé Oxyz, cho A(1;,2;0); B(3;-11). Viét phuong trinh mat cau (S) tam A va ban kinh AB. A. (x-1) +(y-2) +7 = 14. B. (x41) +(y+2) +27=14. C. (x) H(y-2) +2 =14. D. (x-1) +(y+2) +27 =14, Cau 61. (VD)Trong khéng gian voi hé toa dé Oxyz. Hay viet phuong trinh mat cau (S) cé tam 1(2 0,1) va ti€p xuic v6i dudng thang, at. a 2. 2 2 221 2 2 2 21 A. x? +(y+1) +(2+2) =F B. x°+(y-1) +(z-2) > 2 2 2 21 2 2 2 21 C. x +(y-1) +(z-2) a D. x -(y-1) -(z-2) =F x=t Cau 62. (VD) Trong mat phang Oxyz, cho duong thang d:j y=0 va2 mat phang (P) va (Q) lan z=-t luot cé phuong trinh x+3y-z+1=0;x+3y-z—-5=0. Mat cau (S) cé tam I thuéc duong thang (d), tiép xtic voi hai mat phang (P) va (Q) cé phurong trinh A. (x-1)" B. (xf +y?+(e41)'=-5E. c. (x-1f+y?+(e+1)= 5°. Dz (x-1f+y*+(ce1)'=2. Cau 63. Trong khéng gian voi hé toa dé Oxyz, cho ba diém A (2; 0;1),B(1; 0;0),C(1; L 1) va mat phang (P) :x+y+z-2=0. Viét phuong trinh mat cau di qua ba diém A,B,C va cé tam thuéc mat phang (P). A.e+ytxr—-x4+2z41=0. B. x+y tz°-x-2y+1=0. C. xt ty +2?-2x4+2y4+1=0. D. x+y? 4+2?-2x-2z741=0. Cau 64. (S6 GD&DT Nam Dinh - 2017) Trong khéng gian véi hé toa dé Oxyz, cho mat cau x-5 yet zal stl yz do 10 2’ * 12 Viét phurong trinh tat ca cdc mat phang tiép xtc véi mat cau (s) dong thoi song song véi hai duong thang d,, d,. (S):(x-1)' +(y+1) +2=11 va hai dudng thing d,: Trang 7 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 82. Trong khéng gian voi hé toa d6 Oxyz,mat phang (P) qua diém A(L 1,-1) va vudng gd6c duong thang d a = a 5° phuong trinh 1a: A. -x-2y+z+4=0. B. x+2y-4=0. C. x+2y-—z-3=0. D. x+2y+4=0. Cau 83. Trong khéng gian véi hé truc Oxyz, cho A(L; 0;-1),B 3;0;1).Mat phang trung truc doan AB cé phuong trinh 1a A. x+z-2=0. B. x+y-z-2=0. C. xt y-2=0. D. x+z4+1=0. x=t Cau 84. Trong khéng gian voi hé truc Oxyz, cho A(L; 0;-1) va duong thang d: y=1+t Mat z=-1-2t phang (P) qua A va vu6ng gcd cé phirong trinh la: A. x+y-2z-3=0. B. xty+2z-3=0. C. xt+y-2z-1=0. D. x-y-2z-3=0. Cau 85. (TRUONG THPT CHUYEN THAI BiNH) Trong khong gian voi hé truc Oxyz, mat phang di qua diém A(L 3; -2) va song song véi mat phang (P):2x- y+3z+4=01a A. 2x-y+3z+7=0. B. 2xt+y-3z+7=0. C. 2xt+yt+3z+7=0. D. 2x-y+3z-7=0. Cau 86. (THPT XUAN TRUONG C-NAM DINH) Trong khong gian Oxyz, phurong trinh mat phang di qua ba diém A(1;0;0),B(0;2;0),C(0;0;3) la: A. x-y+2z=0. B. x-y+z-2=0. C. x+2y-3z+16=0. D. 6x+3y+2z-6=0. Cau 87. Trong khéng gian voi hé truc toa d6 Oxyz,phuong trinh mat phang di qua ba diém 1(3;-1;5), M(4;2;—-1), N(1;-2;3) la: A. 12x+14y-5z+3=0. B. 12x-14y—5z-25=0. C. 12x+14y-5z-81=0. D. 12x-14y—5z+3=0 . Cau 88. Trong kh6éng gian voi hé truc toa dé Oxyz, goi H(1;2;3) 1a truc tam cua tam giac ABCVéiAB, Cla ba diém Ian luot ndm trén cdc truc Ox,Oy,Oz ( khac géc toa dé). Viet phurong trinh mat phang di qua ba diém A,B,C. A. x+2y+3z-14=0. B. Ttytgeh C. 3x+2y+z-10=0. D. 3x+y+2z-9=0. 3 x=24+t 7, 4 y=3t z=-l+t Cau 89. Trong khéng gian Oxyz, cho hai duong thang d,: . Phuong trinh mat phang chita durong thang, d, vasong song voi dudong thang, d, la: A. 18x+7y+3z-20=0. B. 18x+7y+3z+20=0. C. 18x-7y +3z-34=0. D. 18x-7y+3z+34=0. Cau 90. Trong khéng gian Oxyz, cho bén diém A(-1,3;1),B (1 -1,2),C(2;1;3),D(0;1; -1) . Phuong trinh mat phang chita AB va song song voi CD la: A. x+2z-4=0. B. 2xt+y-1=0. C. 8x+3y—-4z2+3=0. D. x+2y+6z-11=0. Cau 91. Trong khéng gian voi hé toa dd Oxyz, cho hai diém M(1;-1; 5)va N(0; 0,1). Mat phang (a) chita M, N vasong song voi truc Oy co phuong trinh 1a: A. (a):4x-z+1= 0 OB (a):x-42+2= 0 ¢. (a):2x+2-3= 0 Dz. (a):x+4z-1= 0 Cau 92. Mat phang (P) di qua diém G(2; 1 -3) va c&t cdc truc toa dé tai cdc diém A,B, C (khac goc toa do ) sao cho G 1a trong tam cua tam gidc ABC cé phuong trinh la Trang 10 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz A. 3x+6y—2z-18=0.B. 2x+y-3z-14=0. C. xty+z=0. D. 3x+6y-2z-6=0. Cau 93. Trong khéng gian voi hé toa dé Oxyz,phuong trinh mat phang (P) qua hai diém A (GO 1 0),B (2; 3; 1)va vudng gdéc mot mat phang (Q) i+ 2y-z=0 la: A. x+2y-z-2=0. B. 4x-3y—2z+3=0. C.x+2y-z-7=0. D. -4x+3y+2z-5=0. Cau 94. Trong khong gian voi hé toa dé Oxyz,phuong trinh mat phang (P) qua M(3;-1, -5) vudng géc voi hai mat phang (Q) 13x -2y+2z+7=0, (R) :5x- 4y+3z4+1= 01a: A. -2x-y+2z-5=0. B. xt y-z-7=0. C. 2xn+y-—2z-15=0. D. -x-yt+z-7=0. Cau 95. Trong khong gian voi hé truc Oxyz,cho hai mat phang (P):x+ y-2+2=0,(Q):x-3z+1= 0. Mat phang qua A(1;0;1) va vuéng goéc voi hai mat phang (P) va (Q) cé phutong trinh 1a: A. -3x+2y-z+4=0. B. -3x+2y-z+1=0. C. -3x+2y+z+2=0. D. x+2y-z+4=0. Cau 96. Trong khong gian voi hé truc Oxyz,cho hai mat phang (P):x+ y-Z+2= 0,(Q):x-3z+1= 0 .Mat phang qua A(L 0;1) va chtta giao tuyén cua hai mat phang (P) va (Q) cé phutong trinh 1a: A. -3x-y+7z-4=0. B. -3xt+y+7z-4=0. C. -3x-y+7z-1=0. D. -3xt+y+7z-4=0. Cau 97. Trong khéng gian Oxyz, phuong trinh mat phang (P) di qua diém M(-2;3;1) va vudng géc voi hai mat phang (Q): x-3y+2z-1=0, (R):2x+ y-z-1=01a A. (P): x+5y+7z-20=0 B. (P):-2x+3y+z-10=0 C. (P): x+5y+7z+20=0 D. (P): x-3y+2z-1=0 Cau 98. Trong khéng gian voi hé toa dd Oxyz, goi (P)la mat phang di qua diém M(0;2;1)va di qua giao tuyén cua hai mat phang: (a): x+ 5y+9z-13=0 = 0 va (B):3x-y-5z+1=0. Phuong trinh cua (P)la: A. xty+z-3=0 B. 2xt+y+z-3=0 C. x-y+z-3=0. D. 2x-y+z+3=0. Cau 99. Trong khong gian voi hé truc toa dé Oxyz, cho mat cau (S) cd phuong trinh vty +2 -2x+2y4+1=0.Viet phuong trinh (P) di qua hai diém A(0;-1;1),B(1;-2;1) cat mat cAu (S) theo giao tuyén 1a durdng tron cd chu vi bang V2n. A. x+y+3z-2=0,x+y+z=0. B. x+y—-3z2+4=0,x+y-z2+2=0. C. xty+1=0,x+y+42-3=0. D. xt+y+3z-2=0,xt+y-5z+6=0. Cau 100. Trong khéng gian voi hé truc toa dé Oxyz, phuong trinh mat phang di qua A(1;-1;3) vudng géc voi mat phang (Q):x-2y+2z+1=0 va cach géc toa dé mt khoang bang & . A. 38x+y-18z+17=0. B. 38x—- y-18z+17=0. C. 38x+ y+18z—-91=0. D. 4x+y-z=0. Cau 101. Trong khéng gian Oxyz, cho diém M(-1; 2;0) va duong thang attt yt a2 Mat phang (P) di qua M, song song voi dudong thang, d dong thdi khoang cach gitta dudng thang, dva mat phang (P) bang V3 6 phuong trinh la: A. 3x+2y-12z-1=0.B. 3n-2y+z+7=0. C.xtyt5z+1=0. D.x+y—-5z-1=0. Cau 102. Trong khéng gian Oxyz, cho tr dién ABCD cé A (2; 9; 5),B (-3; 10; 13) C(1;-1; 0),D(4 4; 1). Goi (P) 1a mat phang di qua hai diém A, B sao cho khoang cach ttr diém C Trang 11 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz dén mat phang (P) bang khoang cach tlr D dén mat phang (P). Phuong trinh mat phang (P) ; 2x-2y+z-27=0 p|2%t2yt2-27=0 0 Gg x—3y+2+20=07, 3x-y+22-7=0 3x-y+2z-7=0 39x-29y+282+43=0 | 3x-y+2z-7=0 — | 39x-29y+282+43=0 Cau 103. Mat phang nao sau day tiép xuc voi mat cau (S):xt+¥? +27 —2x-4y-6z+5=0 va song song va cach mat phang (P) :x—2y+2z-6 = Om6t khoang lén nhat? A. x-2y+2z+6=0 B.x-2y+2z-12=0 C.x+2y+2z-6=0 D. x-2y+2z-10=0 Cau 104. Trong khéng gian voi hé truc toa d6 Oxyz, mat cau (s) tam. 1(1; 41), ban kinh R=5. Phuong trinh mat phang song song voi mat phang (P):x-2y+ 2z+8=0 va (s)cat theo giao tuyén 1a dwong tron cé chu vi bang 87 1a: A. x-2y+2z+8=0 B.x-2y+2z+4=0 C.x+2y+2z+8=0 D. x+2y+2z+4=0 Cau 105. Trong khéng gian voi hé toa dé Oxyz, cho mat cau (S) cd phuong trinh x +y +2 —2x+4y—6z-11=0 va mat phang (a): 2x + 2y —z +17 = 0. Phuong trinh mat phang (B) song song v6i (a) va cat (S) theo giao tuyén 1a dudng tron cé chu vi bang p=6n. A. 2x+2y-z-7=0. B. 2x+2y-z-6=0. C. 2x+2y-z-5=0. D. 2x+2y-z-4=0. Cau 106. Trong khong gian voi hé toa dé Oxyz, cho A(2; 0; 0) M(1; 1; 1). Mat phang (P) thay déi qua AM cat cdc truc Ox, Oy Ian hot tai B(0; b; 0), C(0; 0; c) (b> 0, c> 0). Phizong trinh mat phang (ABC) sao cho dién tich tam gidc ABC nhé nhat la: A. -3x-2y-z+6=0. B. 2xn+y+z-4=0. C. y-z=0. D. -x+z+2=0. Cau 107. Trong khéng gian voi hé truc Oxyz cho A (0;2;0),B(0; 0;-2),C(1;1;1),D(-1,1, 0) Mat phang (P) qua A vaB thoa man a(c; (P)) = a(D; (P)) cé phuong trinh 1a A. x+2y-2z-4=0. B. -x+2y-2z-4=0. C. x+2y+2z-4=0. D. x-2y-2z-4=0. Cau 108. Trong khong gian voi hé truc Oxyz,cho mat phang (P) :2x-y+3=0 va A (0; 0; 3),B (1 0;2),C(-7; 0;-1) -Mat phang (Q) qua A va vuéng géc mp (P) va cAt BC tai diém Isao cho 11a trung diém BC cé phuong trinh 1a. A. 5x+10y—-6z+18 = 0. B. -x—2y—6z+18=0. C. x-2y—z+3=0. D. 2x+2yt+z+3=0. Cau 109. Trong khéng gian voi hé toa dé Oxyz, cho diém A(2;-1;-2) va dudng thang d cé + x-1 -1 z-l phuong trinh “pst 1 cach ttr d téi (P) 1a 16én nhat . Khi dé, mat phang (P) vudng géc voi mat phang nao sau day ? A. -x+2y+3z+10=0. B. -x+2y+3z-3=0. C. y+z+3=0. D. x-y+z-6=0. Cau 110. Trong khong gian Oxyz, cho ba mat phang (P) ix+y-3z4+1=0, . Goi (P) 1a mat phang di qua A, song song véi dva khoang (Q): 2x+3y+z-1=0, (R):x+2y+4z-2=0. Mat phang (T) chita giao tuyén cua hai mat 23 679 phang (P) va (Q)va tao véi mat phang (R) m6t géc a. Biét cosa = c6 phuong trinh 1a: A. (T):x- y-17z+7 =O hoac (T 53x + 85y+ 65z+ 43=0. B. (T):x-y-17z-7 =O hoac (T 53x + 85y+ 65z- 43=0. Cc. (T):x-y-17z+7 = Ohoac (T):53x+ 85y+ 65z- 43=0. D. (T):x-y-17z-7 =O hoac (T):53x+ 85y+ 652+ 43=0. ): ): Trang 12 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 126. Trong khéng gian voi hé toa d6 Oxyz, cho mat phang (P) :2x+ y+ 2z—-1=0 va duong thang, A: xed oy 2 1 =. Phuong trinh duong thang d di qua diém B(2;-1; 5) song song voi (P) va vudng goc voi Ala A. X=2_ytl 2-5 p x+2_y-1_ 245 6 x+5_yr2_ 2-4 x=5_yt2_2z+4 -5 2 4 -5 2 4 2 -1 5 2 -1 5 Cau 127. Trong khéng gian voi hé toa dé Oxyz, cho duong thang A di qua diém M(0;1;1), x=t vuéng géc voi dudng thang, (4,): y=1-t va cat duong thang (4):$-4 ==, Phuong z=-l trinh cua A 1a: x=0 x=-4 x=0 |= A.yy=l1 B.yy=3 C. jy=14t D.jy=1 z=2-t z=1+t z=1 z=1-t Cau 128. Trong khéng gian voi hé toa d6 Oxyz, cho hai diém A(l; 1 1),B(2; 0; 1) va mat phang (P) ixty+2z+2=0. Viét phuong trinh chinh tac cia duong thang, d di qua A,song song voi mat phang (P) sao cho khoang cach tix B dén d 1én nhat A dwt yet _ ez) BX a¥ Let? 3 1 2 2 2 —2 c gtci_yet_zl . D. x-1_y-1_ 2-1 . 1 1 -1 3 -1 -1 Cau 129. Trong khéng gian voi hé toa d6 Oxyz, cho dudong thang d eR dt SS . Duong thang, d di qua diém M vacé vecto chi phuong a, c6 toa dé la: A. M (2;-1;3),4, = (-2:13). B. M (2;-L-3),a, =(2:-13). C. M(-2:1;3),a, = (2:-13). D. M (2;-1:3),a, =(2:-L-3). Cau 130. Trong kh6éng gian voi hé toa d6 Oxyz, phutong trinh nao sau day 1a phuong trinh tham sé cua dudng thang d qua diém M (-2;3,1) va 66 vecto chi phuong a= (1,-2;2)? x=2+t x=1+2t x=1-2t A. 4 y=-3-2r. B. } y=-2-3¢. C. 4 y=-2432. D. \y=3-2r. z=-1+2t z=2-t za2+t z=1+2t Cau 131. Trong khéng gian voi hé toa d6 Oxyz, phuong trinh nao sau day 1a phuong trinh chinh tac A cua duodng thang di qua hai diém A(1,-2;5)va B(3; 1,1)? A, 221 yt? p 223-371 2 3 1 -2 c Hl yn? _ 245 p, 221 yt? _ “2 3 a) 1 Cau 132. Trong khong gian voi hé toa d6 Oxyz,cho tam giac ABC cd A(-1,3,2),B(2;0;5),C(0,—2;1) . Phuong trinh dung trung tuyén AM cha tam gidc ABC 1a. A x-1l_y+3_z+2 B. Xol_yt3_zt2¢ x+l_y-3_ 7-2 D x-2 y+4 z+l 2 4 -1° 2 -4 1° 2) 4 11 -1 3 Trang 15 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz CHUYEN DE HiNH HOC TOA DO TRONG KHONG GIAN Cau 1. Trong khéng gian Oxyz voi hé toa dé (0; i i) cho OA =-i+3k.Tim toa do diém A A. (-1;0;3) B. (0;-1;3) C. (-1;3;0) D. (-1;3) Cau 2. Trong khéng gian Oxyz, cho diém M(-1;2;3) . Toa d6 hinh chiéu cia M trén truc Ox la: A. (-1,2; 0) B. (-1,0; 0) Cc. (0;0; 3) D. (0; 2;0) Cau 3. Trong khéng gian Oxyz, cho vecto OM =i- V3j+ Ak. Goi M’ 1a hinh chiéu vudng gdc cia M trén mp(Oxy). Khi dé toa dé ctia diém M’ trong hé toa dé Oxyz 1a A. (1;-v3;4) B. (1:4;-V3) Cc. (0;0; 4) D. (1; 4;0) Cau 4. Cho ba diém A(3,1,0); B(2,1,-1); C(x,y,-1). Tinh x,y dé (2-4-3) la trong tam tam gidc ABC A. x=2, y=1 B. x=2, y=-1 C. x=-2, y=-1 D. x=1, y=-5 Cau5. Trong khéng gian Oxyz, cho hinh binh hanh ABCD, biét A(1,0,0); B(0,0,1); C(2,1,1). Toa dé diém D 1a: A. (3,1,0) B. (3;-1;0) C. (-31;0) D. (1;3;0) Cau 6. Cho ba diém A(2,-1,1); B (3,-2, -1) . Tim diém N trén x’Ox cach déu A va B. A. (4;0;0) B. (-4;0;0) C. (1;4;0) D. (2;0;4) Cau7. Trong khéng gian Oxyz, diém M nam trén mat phang(Oxy), cach déu ba diém A (2, -3,1),B(0; 4 3),C(-3; 2; 2) c6 toa dé la: A. [Zo] B. (-3;-6;7) C. (-1;-13;14) D. era) 25° 50 7 14 Cau 8. (De chuyén - Thai Binh — lan 3) Trong khéng gian véi hé toa dé Oxyz, cho A(2; 0; 0), B(0; 3; 1), C(-3; 6; 4). Goi M 1a diém nam trén doan BC sao cho MC = 2MB Dé dai doan AM 1a: A. 27 B. ¥29 C. 3 D. ¥30 Cau9. Trong khéng gian Oxyz, cho ba diém A(2;-1;1), B(-1,3;-1) va C(5,-3;4). Tinh tich vé hung hai vecto ABBC. A. ABBC =48. B. ABBC =-48. C. ABBC =52. D. ABBC =-52. Cau 10. Trong khéng gian Oxyz, cho hai diém M(-1;5;-3), N(7;—-2;—-5) . Tinh dé dai doan MN. A, MN =V13. B, MN =3v13, c, MN=¥109 | Dp. MN=213. Cau ll. Trong khéng gian Oxyz, cho tam gidc ABC cé toa dé cdc dinh A(-4;9;-9), B(2;12;-2) va C(-m—2;,1—m;m+5) . Tim m dé tam gidc ABC vuéng tai B. A, m=3. B, m=-3. Cc, m=4. D, m=-4. Cau 12. Trong khéng gian Oxyz, cho tam gidc ABC cé toa dé cac dinh A(4;2;3), B(1;-2;-9) va C(-1,2; 2) . Xac dinh gid tri z dé tam gidc ABC cn tai A. g=-15 z=15 z=15 g=-15 A. B. Cc. D. z=9 z=-9 z=9 z=-9 Trang 1 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 13. Trong khéng gian Oxyz, cho tam gidc ABC vuéng can tai C va cé caéc dinh A €(Oxz), B(-2;3;1) va C(-1;1;-1). Tim toa d6 diém A. A. A(1,0;-1). B. A(-1,0;1). Cc. A(-1;0;-1). D. A(140;1). Cau 14. Trong khéng gian Oxyz, cho tam gidc ABC cé toa dé cac dinh A(2;1;-1), B(;3;1) va C(3;1;4) . Xac dinh toa d6 diém H 1a chan dudng cao xuat phat tir dinh B cia tam gidc ABC. A. Het 12%) B. He 1) Cc. Ht, By D. HS, 26 = =26 26 26 26 26 26 Cau 15. (Trich $6 GD&DT Binh Thuan). Trong khong gian voi hé truc toa d6 Oxyz, cho hai vecto w= (-3; 1,6) va v= (-1; -1;3) . Tim toa d6 cia vevto [uv] : A. [470 ]= (93:4) B. [130 ]=(9;-3:4) Cc. [4:2 |= (-9:3:4) D. [4:0 |=(9:3;-4) Cau 16. (THPT Kim Lién Ha NGi) Trong khong gian voi hé toa d6 Oxyz,cho ba diém A (2;-1;3), B (4 0;1) va C(-10; 5;3). Vecto nao didi day 1a vecto phap tuyén ctia mat phang (ABC)? _ _ _ A. n,(1;2;0). B. n, (1;2;2). C. n, (1; 8,2). D. n, (1;-2;2). Cau 17. Trong khéng gian voi hé toa dd Oxyz, cho 3 vectoa= (1;2;1),b = (-1;1;2),¢ = (x; 3x;x+2) : 19 -S 26) Ba vecto a,b,c dong phang khi: A. x=-2 B. x=1 C.x=2 D. x=-1 Cau 18. Cho tt dién ABCD biét A(0;0;1),B(2;3;5),C(6; 2;3),D(3;7;2). Thé tich cha tte dién ABCD bang A. 10 B. 20 c. 30 D. 40 Cau 19. Trong khéng gian vdi hé toa dd Oxyz,cho tam giac ABC cd A(2;—1;—2),B(—1;1;2), C(—1;1;0). Tinh dé dai dudng cao xuat phat tr A? a8 B. 2v13, c. Vis D. v3 2 2 Cau 20. Trong khéng gian voi hé toa dd Oxyz, cho 3 diém A (3 3;0),B (3 0;3),C (0;3;3) . Tim toa dé tam dung tron ngoai tiép tam gidc ABC. A. (2;-1;2) B. (2;2;1) C. (2;2;2) D. (-1;2;2) Cau 21. Trong khéng gian Oxyz cho ba vector a, b va é khac 0. Khang dinh nao sai? A. i cung phuong b =[7,b |=0. B. a, b, é déng phang =| i,b ]é=0. C. a,b, 7 khong ding phing @[4,5]é+0 D. a i, @|.cos(a,b}. Cau 22. Trong khéng gian véi hé toa dé Oxyz, cho tam gidc ABC cd A(1;0;0), B(0;0;1), C(2;1;1) . Dién tich cha tam giac ABC bang: a. 38. o . p ZH 2 2 2 2 Cau 23. Trong khéng gian véi hé toa dé Oxyz, cho tte dién ABCD véi A(1;0;0), B(0;1;0), C(0;0;1), D(-2;1;-1). Thé tich cia ti dién ABCD bang: Al B.2 c. >. D. wle Trang 2 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 42. Trong khéng gian voi hé toa dé Oxyz, cho mat cau (S) di qua diém A (1 2;3), B (2; 0; -2) va cé tam nam trén truc Ox. Viét phuong trinh ctia mat cau (S). A. (xt) +(y+2) +27 =29. B. (x+3) +? +2 =29 C2 +y? +(24+3) =29 D. (x-3) +y? +2 =29. Cau 43. Trong khéng gian Oxyz,cho mat phang (P):2x+ y-2z+10=0 va diém 1(2; 1; 3). Phuong trinh mat cau (S) tam I c&t mat phang (P) theo mét didng tron (c) cé ban kinh bang Ala A. (x+-2) +(y+1) +(2+3) =25. B. (x2) +(y-1) +(z-3) =7 C. (x42) +(y-1) +(z-3) =9. D. (x-2) +(y-1) +(2-3) =25. Cau 44. (BE SO GD DT THAI BINH) Cho méat phing (o):4v-2y+3z+1=0 va mat cu (S):x?+¥? +2°—2x+ 4y+ 6z = 0. Khi dé ménh dé nao sau day 14 ménh dé sai: A. (a) 06 diém chung véi (S). B. (a) ct (S) theo mét dudng tron. C. (@) tiép xtc véi (S).D. (@) di qua tam cia (S). Cau 45. (S6 GD&DT Ha Ni) Trong khéng gian Oxyz, cho diém uf p>0) va mat cau (S):a7 + y +2 =8. Dudng thang d thay déi, di qua diém M, cat mat cau (s) tai hai diém A,B phan biét. Tinh dién tich lén nhat $ ctia tam gidc OAB . A. S=y7. B. S=4. Cc. S=27. D. $=2y2. Cau 46. (THPT Hai Ba Trung Lan 2 - Hué 2017) Trong khéng gian Oxyz, cho mat cau (S):(x-1) +(y +3)" +(z-2) =49 va diém M(7;-1,5). Phuong trinh mat phang tip xuic voi mat cau (S) tai diém M 1a: A. x+2y+2z-15=0. B. 6x-2y—2z-34=0.C. 6x+2y+ 3z-55=0.D. 7x-y+5z-55=0. Cau 47. (THPT Chuyén DHSP Ha Noi Lan 3 - 2017) Trong khéng gian voi hé toa dé Oxyz, cho hai diém A(0; -1,0), B(11;-1) va mat cau (S) ity +2? —2x+4y-22-3=0. Mat phang (P) di qua A, B va cAt mat cau (S) theo giao tuyén 1a dudng tron cé ban kinh lén nhat cé phuong trinh 1a A. x-2y+3z-2=0. B. x-2y-3z-2=0. C. x+2y-3z-6=0. D. 2x-y-1=0. Cau 48. (THPT Chuyén Lam Son Thanh Hoa - 2017) Trong khong gian voi hé toa d6 Oxyz, cho diém 1(2; 41) va mat phang (P) :x+y+z—4=0. Tim phuong trinh mat cau (S) cé tam I sao cho (S) cAt mat phang (P) theo m6t durong tron cé duong kinh bang 2. A. (x42) +(yt4) +(z41) =4. B. (x-2) +(y-4) +(z-1) =4. C. (x-2) +(y-4y +(z-1) =3. D. (x-1) +(y+2) +(z-4) =3. Cau 49. (S6 GD&DT Thanh Hoa - 2017) Trong khéng gian voi hé toa dé Oxyz, cho duong x-2 y-1 z+1 So va diém 1(2;-1;1). Viét phuong trinh mat cau cé tam I va cat duong thang d tai hai diém A,B sao cho tam gidc IAB vudng tai I. thang, d: Trang 5 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz A. (x-2) +(y+1) +(2-1) =8. B. (x-2)'+(y+1) +(z-1) -2. C. (x-2)'+(ytl) +(z-1) =9. D. (x+2)'+(y-1) +(z+1) =9. Cau 50. (THPT Ha Huy Tap Lan 1 - Ha Tinh - 2017) Trong khéng gian Oxyz, cho diém M(2;1,1), mat phang(a):x+y+z-4=0 va mat cau (S):x° +? + 2? - 6x- 6y-8z+18=0. Phuong trinh duong thang A di qua M va nam trong (a) cat mat cau (s) theo mét doan thang cé 46 dai nhé nhat 1a: A. x-2_ y-1_z-1p x=2_ y-1_ z-1 c x=2_ y-1_z-1 py x-2_ y-1_ 2-1 -2 1 1 1 -2 1 1 2 -3 1 1 -2 Cau 51. Trong khéng gian voi hé toa dd Oxyz, cho mat cau (S):(x-5) +(y+4y +27 =9. Hay fim toa dé tam I va bankinh R ctia mat cau (S)? A. 1(5;4;0),R=3. — B. I(-5;4;0),R=9. C. 1(5;-4;0),R=9. D. 1(5;-4;0),R=3. Cau 52. ( DE THI THU NGHIEM BGD 2017) Trong khéng gian voi hé toa d6 Oxyz, phuong trinh nao dui day 1a phuong trinh cua mat cau cé tam 1(1;2; -1) va tiép xuc voi mat phang (P):x-2y-2z-8 =0? A. (x41) +(y+2) +(2-1) =3. B. (x-1)' +(y-2) +(z+1) =3. C. (x=1) +(y-2) +(z+1) =9. D. (x+1) +(y+2) +(z-1) =9. Cau 53. Mat cau di qua bén diém A (6;-2;3),B(0;1;6),C(2;0;-1),D(4;1;0) cé phuong trinh la: A. +y +27 4+4x-2y+6z-3=0. B. 2° +? +2°-4x+2y-6z-3=0. Cty +2? — 4x4 2y-6z-3=0. D. x+y? +2°- 4x4 2y-6z4+3=0. Cau 54. Trong khong gian voi hé toa dé Oxyz, cho diém A(2; -1;0) va mat phang (P):x-2y+z+2= 0.Goi I 1a hinh chiéu vudéng géc cua A trén mat phang (P). Phuong trinh mat c4u di qua A vacé tam I la: A. (x1) +(y+1) +(z41) =6. B. (x+1) +(y-1) +(z+1) =6. C. (x1) +(y-1) +(z41)° =6. D. (x+1) +(y+1) +(z-1) =6. x=t Cau 55. Cho d:;y=-l va 2 mat phang (a):x+2y+2z+3=0;(B):x+2y+2z+7 =0.Viet Z=-t phuong trinh mat cau cé tam I thuéc dung thang d va tiép xtic voi hai mat phang (z),(B)- A. (-3) (y+) +(243) = 5, B.xte(y-tp +2 5. 4 4 Cc. M4(ytl) t2*= 5. D. (x43) Hy tI) +(2-3)'=5. Cau 56. Trong khéng gian véi hé toa dé Oxyz cho ba diém A(a;0;0),B(0;b;0),C(0;0;c) voi a,b,c la cdc s6 thizc duong thay déi thoa man 24 2o1, Ki hiéu (S) Ja mat cau cé tam 1a a c gdc toa dd O, tiép xc vi mat phang (ABC) . Tim ban kinh lén nhat cua (5). AL3. B. V5. C. 25. D. 9. Trang 6 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 57. (NB) Trong khéng gian voi hé truc toa dd Oxyz, phuong trinh mat cau (S) cé tam 1(1;2;3) , ban kinh r= 2 c6é phuong trinh 1a: A. (x-1)' +(y-2) +(z-3) =2. B, (x41) +(y+2) +(24+3) =4. C. (x+1)'-(y+2) -(243) =4. D. (x-1) +(y-2)' + (2-3) =4. Cau 58. (NB) Trong khéng gian vi hé truc toa d6 Oxyz, xac dinh toa dé tam I va ban kinhr cua mat cau (S).x° + y?+ 2? -2x+6y-8z+1=0 A. I(1-3;4);r=5. B. I(-1;3;-4);r =5 C. 1(1;-3;4);r = 25 D. I(1;-3;4);r=-5. Cau 59. (TH) Trong khong gian voi hé truc toa d6 Oxyz, phurong trinh nao dudi day 14 phuong trinh cha mat cau cé tam I(-1;1;2) va tiép xtc voi mat phang (P):2x- y-3z-5=02 A. (x-1)'+(y+1) +(2+2) =V14. B. (x+1) +(y-1) +(z-2) =14. C. (x+1)'-(y-1) -(2-2) =14. D. (x+1)+(y-1)+(z-2)=14. Cau 60. (TH- Dé khao sat tinh Quang Ninh-2017) Trong khéng gian véi hé truc toa dé Oxyz, cho A(1;,2;0); B(3;-11). Viét phuong trinh mat cau (S) tam A va ban kinh AB. A. (x-1) +(y-2) +7 = 14. B. (x41) +(y+2) +27=14. C. (x) H(y-2) +2 =14. D. (x-1) +(y+2) +27 =14, Cau 61. (VD)Trong khéng gian voi hé toa dé Oxyz. Hay viet phuong trinh mat cau (S) cé tam 1(2 0,1) va ti€p xuic v6i dudng thang, at. a 2. 2 2 221 2 2 2 21 A. x? +(y+1) +(2+2) =F B. x°+(y-1) +(z-2) > 2 2 2 21 2 2 2 21 C. x +(y-1) +(z-2) a D. x -(y-1) -(z-2) =F x=t Cau 62. (VD) Trong mat phang Oxyz, cho duong thang d:j y=0 va2 mat phang (P) va (Q) lan z=-t luot cé phuong trinh x+3y-z+1=0;x+3y-z—-5=0. Mat cau (S) cé tam I thuéc duong thang (d), tiép xtic voi hai mat phang (P) va (Q) cé phurong trinh A. (x-1)" B. (xf +y?+(e41)'=-5E. c. (x-1f+y?+(e+1)= 5°. Dz (x-1f+y*+(ce1)'=2. Cau 63. Trong khéng gian voi hé toa dé Oxyz, cho ba diém A (2; 0;1),B(1; 0;0),C(1; L 1) va mat phang (P) :x+y+z-2=0. Viét phuong trinh mat cau di qua ba diém A,B,C va cé tam thuéc mat phang (P). A.e+ytxr—-x4+2z41=0. B. x+y tz°-x-2y+1=0. C. xt ty +2?-2x4+2y4+1=0. D. x+y? 4+2?-2x-2z741=0. Cau 64. (S6 GD&DT Nam Dinh - 2017) Trong khéng gian véi hé toa dé Oxyz, cho mat cau x-5 yet zal stl yz do 10 2’ * 12 Viét phurong trinh tat ca cdc mat phang tiép xtc véi mat cau (s) dong thoi song song véi hai duong thang d,, d,. (S):(x-1)' +(y+1) +2=11 va hai dudng thing d,: Trang 7 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 82. Trong khéng gian voi hé toa d6 Oxyz,mat phang (P) qua diém A(L 1,-1) va vudng gd6c duong thang d a = a 5° phuong trinh 1a: A. -x-2y+z+4=0. B. x+2y-4=0. C. x+2y-—z-3=0. D. x+2y+4=0. Cau 83. Trong khéng gian véi hé truc Oxyz, cho A(L; 0;-1),B 3;0;1).Mat phang trung truc doan AB cé phuong trinh 1a A. x+z-2=0. B. x+y-z-2=0. C. xt y-2=0. D. x+z4+1=0. x=t Cau 84. Trong khéng gian voi hé truc Oxyz, cho A(L; 0;-1) va duong thang d: y=1+t Mat z=-1-2t phang (P) qua A va vu6ng gcd cé phirong trinh la: A. x+y-2z-3=0. B. xty+2z-3=0. C. xt+y-2z-1=0. D. x-y-2z-3=0. Cau 85. (TRUONG THPT CHUYEN THAI BiNH) Trong khong gian voi hé truc Oxyz, mat phang di qua diém A(L 3; -2) va song song véi mat phang (P):2x- y+3z+4=01a A. 2x-y+3z+7=0. B. 2xt+y-3z+7=0. C. 2xt+yt+3z+7=0. D. 2x-y+3z-7=0. Cau 86. (THPT XUAN TRUONG C-NAM DINH) Trong khong gian Oxyz, phurong trinh mat phang di qua ba diém A(1;0;0),B(0;2;0),C(0;0;3) la: A. x-y+2z=0. B. x-y+z-2=0. C. x+2y-3z+16=0. D. 6x+3y+2z-6=0. Cau 87. Trong khéng gian voi hé truc toa d6 Oxyz,phuong trinh mat phang di qua ba diém 1(3;-1;5), M(4;2;—-1), N(1;-2;3) la: A. 12x+14y-5z+3=0. B. 12x-14y—5z-25=0. C. 12x+14y-5z-81=0. D. 12x-14y—5z+3=0 . Cau 88. Trong kh6éng gian voi hé truc toa dé Oxyz, goi H(1;2;3) 1a truc tam cua tam giac ABCVéiAB, Cla ba diém Ian luot ndm trén cdc truc Ox,Oy,Oz ( khac géc toa dé). Viet phurong trinh mat phang di qua ba diém A,B,C. A. x+2y+3z-14=0. B. Ttytgeh C. 3x+2y+z-10=0. D. 3x+y+2z-9=0. 3 x=24+t 7, 4 y=3t z=-l+t Cau 89. Trong khéng gian Oxyz, cho hai duong thang d,: . Phuong trinh mat phang chita durong thang, d, vasong song voi dudong thang, d, la: A. 18x+7y+3z-20=0. B. 18x+7y+3z+20=0. C. 18x-7y +3z-34=0. D. 18x-7y+3z+34=0. Cau 90. Trong khéng gian Oxyz, cho bén diém A(-1,3;1),B (1 -1,2),C(2;1;3),D(0;1; -1) . Phuong trinh mat phang chita AB va song song voi CD la: A. x+2z-4=0. B. 2xt+y-1=0. C. 8x+3y—-4z2+3=0. D. x+2y+6z-11=0. Cau 91. Trong khéng gian voi hé toa dd Oxyz, cho hai diém M(1;-1; 5)va N(0; 0,1). Mat phang (a) chita M, N vasong song voi truc Oy co phuong trinh 1a: A. (a):4x-z+1= 0 OB (a):x-42+2= 0 ¢. (a):2x+2-3= 0 Dz. (a):x+4z-1= 0 Cau 92. Mat phang (P) di qua diém G(2; 1 -3) va c&t cdc truc toa dé tai cdc diém A,B, C (khac goc toa do ) sao cho G 1a trong tam cua tam gidc ABC cé phuong trinh la Trang 10 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz A. 3x+6y—2z-18=0.B. 2x+y-3z-14=0. C. xty+z=0. D. 3x+6y-2z-6=0. Cau 93. Trong khéng gian voi hé toa dé Oxyz,phuong trinh mat phang (P) qua hai diém A (GO 1 0),B (2; 3; 1)va vudng gdéc mot mat phang (Q) i+ 2y-z=0 la: A. x+2y-z-2=0. B. 4x-3y—2z+3=0. C.x+2y-z-7=0. D. -4x+3y+2z-5=0. Cau 94. Trong khong gian voi hé toa dé Oxyz,phuong trinh mat phang (P) qua M(3;-1, -5) vudng géc voi hai mat phang (Q) 13x -2y+2z+7=0, (R) :5x- 4y+3z4+1= 01a: A. -2x-y+2z-5=0. B. xt y-z-7=0. C. 2xn+y-—2z-15=0. D. -x-yt+z-7=0. Cau 95. Trong khong gian voi hé truc Oxyz,cho hai mat phang (P):x+ y-2+2=0,(Q):x-3z+1= 0. Mat phang qua A(1;0;1) va vuéng goéc voi hai mat phang (P) va (Q) cé phutong trinh 1a: A. -3x+2y-z+4=0. B. -3x+2y-z+1=0. C. -3x+2y+z+2=0. D. x+2y-z+4=0. Cau 96. Trong khong gian voi hé truc Oxyz,cho hai mat phang (P):x+ y-Z+2= 0,(Q):x-3z+1= 0 .Mat phang qua A(L 0;1) va chtta giao tuyén cua hai mat phang (P) va (Q) cé phutong trinh 1a: A. -3x-y+7z-4=0. B. -3xt+y+7z-4=0. C. -3x-y+7z-1=0. D. -3xt+y+7z-4=0. Cau 97. Trong khéng gian Oxyz, phuong trinh mat phang (P) di qua diém M(-2;3;1) va vudng géc voi hai mat phang (Q): x-3y+2z-1=0, (R):2x+ y-z-1=01a A. (P): x+5y+7z-20=0 B. (P):-2x+3y+z-10=0 C. (P): x+5y+7z+20=0 D. (P): x-3y+2z-1=0 Cau 98. Trong khéng gian voi hé toa dd Oxyz, goi (P)la mat phang di qua diém M(0;2;1)va di qua giao tuyén cua hai mat phang: (a): x+ 5y+9z-13=0 = 0 va (B):3x-y-5z+1=0. Phuong trinh cua (P)la: A. xty+z-3=0 B. 2xt+y+z-3=0 C. x-y+z-3=0. D. 2x-y+z+3=0. Cau 99. Trong khong gian voi hé truc toa dé Oxyz, cho mat cau (S) cd phuong trinh vty +2 -2x+2y4+1=0.Viet phuong trinh (P) di qua hai diém A(0;-1;1),B(1;-2;1) cat mat cAu (S) theo giao tuyén 1a durdng tron cd chu vi bang V2n. A. x+y+3z-2=0,x+y+z=0. B. x+y—-3z2+4=0,x+y-z2+2=0. C. xty+1=0,x+y+42-3=0. D. xt+y+3z-2=0,xt+y-5z+6=0. Cau 100. Trong khéng gian voi hé truc toa dé Oxyz, phuong trinh mat phang di qua A(1;-1;3) vudng géc voi mat phang (Q):x-2y+2z+1=0 va cach géc toa dé mt khoang bang & . A. 38x+y-18z+17=0. B. 38x—- y-18z+17=0. C. 38x+ y+18z—-91=0. D. 4x+y-z=0. Cau 101. Trong khéng gian Oxyz, cho diém M(-1; 2;0) va duong thang attt yt a2 Mat phang (P) di qua M, song song voi dudong thang, d dong thdi khoang cach gitta dudng thang, dva mat phang (P) bang V3 6 phuong trinh la: A. 3x+2y-12z-1=0.B. 3n-2y+z+7=0. C.xtyt5z+1=0. D.x+y—-5z-1=0. Cau 102. Trong khéng gian Oxyz, cho tr dién ABCD cé A (2; 9; 5),B (-3; 10; 13) C(1;-1; 0),D(4 4; 1). Goi (P) 1a mat phang di qua hai diém A, B sao cho khoang cach ttr diém C Trang 11 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz dén mat phang (P) bang khoang cach tlr D dén mat phang (P). Phuong trinh mat phang (P) ; 2x-2y+z-27=0 p|2%t2yt2-27=0 0 Gg x—3y+2+20=07, 3x-y+22-7=0 3x-y+2z-7=0 39x-29y+282+43=0 | 3x-y+2z-7=0 — | 39x-29y+282+43=0 Cau 103. Mat phang nao sau day tiép xuc voi mat cau (S):xt+¥? +27 —2x-4y-6z+5=0 va song song va cach mat phang (P) :x—2y+2z-6 = Om6t khoang lén nhat? A. x-2y+2z+6=0 B.x-2y+2z-12=0 C.x+2y+2z-6=0 D. x-2y+2z-10=0 Cau 104. Trong khéng gian voi hé truc toa d6 Oxyz, mat cau (s) tam. 1(1; 41), ban kinh R=5. Phuong trinh mat phang song song voi mat phang (P):x-2y+ 2z+8=0 va (s)cat theo giao tuyén 1a dwong tron cé chu vi bang 87 1a: A. x-2y+2z+8=0 B.x-2y+2z+4=0 C.x+2y+2z+8=0 D. x+2y+2z+4=0 Cau 105. Trong khéng gian voi hé toa dé Oxyz, cho mat cau (S) cd phuong trinh x +y +2 —2x+4y—6z-11=0 va mat phang (a): 2x + 2y —z +17 = 0. Phuong trinh mat phang (B) song song v6i (a) va cat (S) theo giao tuyén 1a dudng tron cé chu vi bang p=6n. A. 2x+2y-z-7=0. B. 2x+2y-z-6=0. C. 2x+2y-z-5=0. D. 2x+2y-z-4=0. Cau 106. Trong khong gian voi hé toa dé Oxyz, cho A(2; 0; 0) M(1; 1; 1). Mat phang (P) thay déi qua AM cat cdc truc Ox, Oy Ian hot tai B(0; b; 0), C(0; 0; c) (b> 0, c> 0). Phizong trinh mat phang (ABC) sao cho dién tich tam gidc ABC nhé nhat la: A. -3x-2y-z+6=0. B. 2xn+y+z-4=0. C. y-z=0. D. -x+z+2=0. Cau 107. Trong khéng gian voi hé truc Oxyz cho A (0;2;0),B(0; 0;-2),C(1;1;1),D(-1,1, 0) Mat phang (P) qua A vaB thoa man a(c; (P)) = a(D; (P)) cé phuong trinh 1a A. x+2y-2z-4=0. B. -x+2y-2z-4=0. C. x+2y+2z-4=0. D. x-2y-2z-4=0. Cau 108. Trong khong gian voi hé truc Oxyz,cho mat phang (P) :2x-y+3=0 va A (0; 0; 3),B (1 0;2),C(-7; 0;-1) -Mat phang (Q) qua A va vuéng géc mp (P) va cAt BC tai diém Isao cho 11a trung diém BC cé phuong trinh 1a. A. 5x+10y—-6z+18 = 0. B. -x—2y—6z+18=0. C. x-2y—z+3=0. D. 2x+2yt+z+3=0. Cau 109. Trong khéng gian voi hé toa dé Oxyz, cho diém A(2;-1;-2) va dudng thang d cé + x-1 -1 z-l phuong trinh “pst 1 cach ttr d téi (P) 1a 16én nhat . Khi dé, mat phang (P) vudng géc voi mat phang nao sau day ? A. -x+2y+3z+10=0. B. -x+2y+3z-3=0. C. y+z+3=0. D. x-y+z-6=0. Cau 110. Trong khong gian Oxyz, cho ba mat phang (P) ix+y-3z4+1=0, . Goi (P) 1a mat phang di qua A, song song véi dva khoang (Q): 2x+3y+z-1=0, (R):x+2y+4z-2=0. Mat phang (T) chita giao tuyén cua hai mat 23 679 phang (P) va (Q)va tao véi mat phang (R) m6t géc a. Biét cosa = c6 phuong trinh 1a: A. (T):x- y-17z+7 =O hoac (T 53x + 85y+ 65z+ 43=0. B. (T):x-y-17z-7 =O hoac (T 53x + 85y+ 65z- 43=0. Cc. (T):x-y-17z+7 = Ohoac (T):53x+ 85y+ 65z- 43=0. D. (T):x-y-17z-7 =O hoac (T):53x+ 85y+ 652+ 43=0. ): ): Trang 12 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 126. Trong khéng gian voi hé toa d6 Oxyz, cho mat phang (P) :2x+ y+ 2z—-1=0 va duong thang, A: xed oy 2 1 =. Phuong trinh duong thang d di qua diém B(2;-1; 5) song song voi (P) va vudng goc voi Ala A. X=2_ytl 2-5 p x+2_y-1_ 245 6 x+5_yr2_ 2-4 x=5_yt2_2z+4 -5 2 4 -5 2 4 2 -1 5 2 -1 5 Cau 127. Trong khéng gian voi hé toa dé Oxyz, cho duong thang A di qua diém M(0;1;1), x=t vuéng géc voi dudng thang, (4,): y=1-t va cat duong thang (4):$-4 ==, Phuong z=-l trinh cua A 1a: x=0 x=-4 x=0 |= A.yy=l1 B.yy=3 C. jy=14t D.jy=1 z=2-t z=1+t z=1 z=1-t Cau 128. Trong khéng gian voi hé toa d6 Oxyz, cho hai diém A(l; 1 1),B(2; 0; 1) va mat phang (P) ixty+2z+2=0. Viét phuong trinh chinh tac cia duong thang, d di qua A,song song voi mat phang (P) sao cho khoang cach tix B dén d 1én nhat A dwt yet _ ez) BX a¥ Let? 3 1 2 2 2 —2 c gtci_yet_zl . D. x-1_y-1_ 2-1 . 1 1 -1 3 -1 -1 Cau 129. Trong khéng gian voi hé toa d6 Oxyz, cho dudong thang d eR dt SS . Duong thang, d di qua diém M vacé vecto chi phuong a, c6 toa dé la: A. M (2;-1;3),4, = (-2:13). B. M (2;-L-3),a, =(2:-13). C. M(-2:1;3),a, = (2:-13). D. M (2;-1:3),a, =(2:-L-3). Cau 130. Trong kh6éng gian voi hé toa d6 Oxyz, phutong trinh nao sau day 1a phuong trinh tham sé cua dudng thang d qua diém M (-2;3,1) va 66 vecto chi phuong a= (1,-2;2)? x=2+t x=1+2t x=1-2t A. 4 y=-3-2r. B. } y=-2-3¢. C. 4 y=-2432. D. \y=3-2r. z=-1+2t z=2-t za2+t z=1+2t Cau 131. Trong khéng gian voi hé toa d6 Oxyz, phuong trinh nao sau day 1a phuong trinh chinh tac A cua duodng thang di qua hai diém A(1,-2;5)va B(3; 1,1)? A, 221 yt? p 223-371 2 3 1 -2 c Hl yn? _ 245 p, 221 yt? _ “2 3 a) 1 Cau 132. Trong khong gian voi hé toa d6 Oxyz,cho tam giac ABC cd A(-1,3,2),B(2;0;5),C(0,—2;1) . Phuong trinh dung trung tuyén AM cha tam gidc ABC 1a. A x-1l_y+3_z+2 B. Xol_yt3_zt2¢ x+l_y-3_ 7-2 D x-2 y+4 z+l 2 4 -1° 2 -4 1° 2) 4 11 -1 3 Trang 15 | Nh6m Dé file word Chuyén dé Oxyz yt+2_z-3 va x72 _ 2 -1 1 x-1_yt2_ X+1_ y+2_ 243 D x-1_ 3 —5 3 5 1 —2 3 =-3+2t ang d: t Phuong trinh -14+4t Nh6m Dé file word Cau 133. Trong khéng gian voi hé toa d6 Oxyz, cho hai duong thang d,:——=-——= Phuong trinh dudng thang, A di qua diém A(1;2;3) vudng géc voi d, yt3_ z+5 _ z+ z43 Cc -l1 za4 zt+4 D. x+4_ yt2_ 3 2 -1 x=l+t x Cau 134. Trong khong gian voi hé toa dé Oxyz, cho duong thang y chinh tac cha dudng thang di qua diém A(-4;-2;4) cat va vudng géc voi dla 2 _zt+4 c x74 yr2_ 3 —2 1 z=3tt A. x73_yr2_ z+ B x74_ yo _ 4° 20 «4 3 2 -1 cho duong thang (A) cd phuong trinh tham so , y=2-2r , Cau 135. Trong khong gian O. 41 Dz 1 Khi dé duong thang (A) cé phuong trinh chinh tac 1a A Xt] y+2_ 243 B. xt1_yt2_z+3 ¢ Xt+1_y-2_ 1 2 1 1 2 1 1 2 3 Cu 136. Phuong trinh tham sé ctia dudng thang d di quadiém A(x); yz) va cd vecto chi phtrong u=(a b,c) la X=Xx,+bt X=xX,+ct X=Xx,+at X=X,+bt y=yotet- B.d:iy=y tht. C. d:iy=yjtbt. D.d:iy=yy-ct- C Z=%4tct Z=%t+ at Phuong trinh chinh tac cha duong thang d di qua diém A(x; yy3%) va 6 vecto chi =o _ 27% A.d: Cau 137. phuong w= (a;b;c) 1a A, ditto 22 t¥0 2 Et a b b =o _% x=2+t l+¢(teR). z=3tt C. d: a Cau 138. Duong thang nao sau day song song voi durong thang ; y =1+2r 3 c. “=D. 1 1 x= 2t A.jy=t B.)y=1-t zZ=-3t z=14+3t Cau 139. Trong khéng gian voi hé toa dé Oxyz cho duong thang d qua hai diém M (2: 0,5) N (1, 1,3). Vecto chi phttong cia dung thang d 1a B. w= (2;0;5) C. w= (413) D. w= G:18) Cau 140. Trong khéng gian Oxyz cho M (2: 3 1) va mat phang( ) x+3y—z+2=0 . Duong z 2) A. w=(-L1-2) thang d qua diém M, vudng géc voi mat phang ( ) cé phuong trinh 1a Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz x=2+3t x=2+t x=2+t x=2-t A. }y=-3+1t,teR B. } y=-3-1t,teR C. )y=-34+3r,reR D.)y=-3+3¢,teR z=l-t z=14+3t z=l-t zal+t Cau 141. Trong khéng gian voi hé toa dd Oxyz cho hai mp (P): x-2y+z-2=0 va (Q) :2x+y—-z+1=0. Phuong trinh dung d 1a giao tuyén cua (P) va (Q) cé dang: x=l+t x=l 1 2 A. | y=3r B. | y=3-1 c, *=2¥ 22 p, 22225 1 3 5 3 1S g=1-5t c=5 Cau 142. (Dé suu tam va bién #P) Trong khéng gian véi hé toa dé Oxy, cho diém A(1; 2; 3) va duong thang d: tS 2 . Viét phuong trinh dudng thang A di qua diém A, vuéng géc voi duong thang diva c&t truc Ox. A.22 1 ar 2 -2:3 B. X22_yr?_ 2-3 x+1 yt? 23 p. xX+2 _yt2_ 2430 2 2 3 1 2 3 2 2 3 1 2 3 Cau 143. Cho Trong khéng gian voi hé toa d6 Oxyz, cho hai mat phang (Q) :xty-zt+1=0 va (P) :(2m-1)x+3y-(m+1)z+9-3m = 0. Gia tri nao cua tham sé m dé hai mat phang (P) va (2) song song? A.m=1. B.m#l. Cc. VmeR. D. Khéng t6n tai s6 m. Cau 144. Trong khéng gian véi hé toa d6 Oxyz, cho hai mat phang (P) :3x+4y—2z—-1=0 va (Q) :x+2y+2z—3=0. Biét mat phang (P) cAt mat phang (Q) theo giao tuyén 1a mét dudng thang, d. Khi dé mét vécto chi phuong cua durong thang, dla: A. a =(6;-4;1). B. ta =(6;4;1). C. wa=(3:4;1). Ds a «= (6-43) = y-1_z4+1., Cau 145. Trong khéng gian voi hé toa d6 Oxyz, cho hai duong thang, A:——= WA va x=1+2t d:}y=—1+2t,t€R. Khang dinh nao sau day 1a khang dinh dung ? z=1+t A.A c&td va A vuéng gécvoi d. B. A va d chéo nhau, A vuéng gécvoi d. C. A cat d va A khong vuéng géc voi d. D. A va d chéo nhung khéng vudng g6C. Cau 146. Trong khéng gian voi hé toa dé Oxyz, cho hai duong thang Aw 1 "=" x=1+6t va d:yy =3-6t. Tinh gia tri biéu thitc K =m? +n’, biét hai dudng thang, A va d tring nhau z2=6-3t A. K = 30. B. Kk = 45. C.K =55. D. kK =73. Cau 147. Trong khéng gian voi hé toa dé Oxyz, cho phuong trinh hai mat cau cé dang (S):x° +y? +27 4x -6y—22-2=0 va (S/):x? +y? +2*-6x—2y—6z-30=0. Khang dinh nao sau day la khang dinh dung ? A. (S) cat (s’). B. (S) tiép xtic trong véi (s’). Trang 17 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz Cau 162. Trong khéng gian véi hé toa dé Oxyz, cho diém A(0;0;—2) va duong thang . Lap phuong trinh mat cau tam A, cat A tai hai diém Bva C sao cho A x+2_ y-2_ — 2 3 BC=8? AXt+y te =25. B. V4 ¥4(z4+2) =25. C. (x +2) +(y—3) +(z+1) =25 D. (x42) +242? =25, Cau 163. Trong khéng gian voi hé toa d6 Oxyz cho mat phang (a):(m—1)x+2y—32-7 = 0 song song véi mat phang (8) :-6x +(n +l)y +6z+3=0. Khi dé tinh gia tri cua m va n? A.m=4;n=-5 B. m=5;n=-4 C. m=4n=5. D. m=—4;n=-5 Cau 164. Trong khéng gian voi hé toa dé Oxyz cho hai mat phang cé phuong trinh (a) mx — y +(e? —2)z +2=0 va (8) :2x+m’y—2z+1=0. Diéu kién cha m dé (2) vudéng goc voi (8) 1a? A. [nl =2 . B. |m|=1 . C. |ml= v2 D. |mm| = V3 Cau 165. Trong khéng gian voi hé toa d6 Oxyz cho hai durong phang cé phuong trinh Tan luot tad, SPP 8 SLY 24) yy aigin A(1;2;3) . Duong thing A di 2 -1 1 -1 2 1 qua A ,vudng géc voi d, va cat d, cé phuong trinh 1a? x-1_y-2_ 2-3 B x-1_y-2_ 2-3 A. . 1 -3 -5 -1 -3 -5 c xXr1_yn2_ 2-3 — x-1_y-2_ 2-3 1 3 5 1 3 -5 Cau 166. Trong khéng gian voi hé toa dd Oxyz cho dudng thang, d, aot = t = atl va x=-l-t d,:4y=0 . Ménh dé nao sau day dung? z=3+4+2t A. d, vuéng géc va khong cat voi d, B. d, cat va khong vusng géc voi d, Cc. d, cat va vuong goéc voi d, D. d, chéo va vung géc voi d, . Cau 167. Trong khéng gian voi hé toa d6 Oxyz cho mat cau (s) : (x -1y + (y-2) + (z -3) =4. Viet phuong trinh mat phang (P) chita truc Ox va cat (s) theo giao tuyén 1a mot duong tron co ban kinh bang 2? A. 3y—2z=0 B. 2y—3z=0. C. 2y+3z=0. D. 3y+2z=0. Cau 168. Trong khéng gian véi hé toa dd Oxyz cho diém 1(-12; 1) va mat phang (P) :2x—y+2z—7=0 . Viét phuong trinh mat c4u cé tam I va tiép xuic véi mat phang (P) ? A. (8):(x+1) +(y-2) + (2-1) =3 B. (8):(x-1) +(y+2) +(2+1) =9. C. (8):(x-1) +(y+2) +(z+1) =3. D. (5):(x+1) +(y—2) +(z-1) =9. Cau 169. Trong khéng gian vdi hé toa dé Oxyz cho mat cau (s) : (x -1) + (y-1y) + (z+2)" =4 va diém A(l; 1 -1) . Ba mat phang thay déi di qua A va di mét vudng géc cat mat cau (s Trang 20 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz theo ba giao tuyén 1a cdc dudng tron (c,), (C,), (C,)- Tinh tong dién tich cia ba hinh tron (C1), (Ca), (Ca)? A. 4x B. 127. C. lin. D. 37. Cau 170. Cho hai mat phang cé phuong trinh: 2x-my+3z-6=0 va mx—2y+ (m+ 1)z- 10=0. Voi m=2 thi hai mat phang nay? A. song song voi nhau. B. trung nhau. C. cat nhau nhung khong vuéng g6C. D. vuéng goc véi nhau. Cau 171. Trong khéng gian voi hé toa d6 Oxyz, cho hai mat phang (P):2x+my+3z-5=0 va (Q):nx—-6y-6z+2=0.Tim cac gid tri cua m va ndé (P)//(Q)? A. m=3; n=-4. B. m=-3; n=4. C. m=3;n=4. D. m=1; n=-2. x=1+2t Cau 172. Trong khong gian voi hé toa dé Oxyz, cho hai duong thang d,:\ y=-14+3t z=5+t x=1+3t' d, :4 y=-2+2t'. Ménh dé nao sau day 1a dung? z=-1+28' A. d, va d, chéo nhau. B. d, va d, cat nhau. C. d, va d, tring nhau. D. d, va d, song song vi nhau. x=2+mt Cau 173. Trong khéng gian voi hé toa dé Oxyz, cho duong thang (2) syy=nt+3t va mat phang z=1-2t (P) :2x+y—z+3=0. Xac dinh gid tricia m,n sao cho dc(P)? 5 5 5 AMS 9, B79. ceo. Dz ren. n=-6 nz—6 neR ~ Cau 174. Mat phang nao sau day tiép xtic voi mat cau (s) : (x+ 2) +y° +(@-2)° =9? A. 4x+3y—7=0. B. 4x+3y+7=0. C. 4x+3z-7=0. D. 4x+3z-7=0. Cau 175. Trong khéng gian voi hé toa dé Oxyz, cho mat phang (P) :x—y+2z—6=0 va mat cau: (S) rx? +y? +2° —2x—2y —7 =0, biét mat phang (P) cAt mat cau (s) theo giao tuyén la dudng tron (c) - Tinh ban kinh r cua dong tron (c) ? A. r=v3. B.r=3. r=V6. D. r=6. Cau 176. Trong khéng gian véi hé toa dé Oxyz, cho mat cAu (S) cd tam I thudc dudng thang Aka ¥t 3 T peat. Biét rang mat cau (S) cé ban kinh bang 22 va cat mat phang (Oxz) theo m6t dung tron cé ban kinh bang 2. Tim toa dé cia I? A. I(5; 2; 10), 1(0; —3; 0). B. I(1; —2; 2), 1(0; —3; 0). C. 1(1; —2; 2), (3; 2; 10). D. I(1; —2; 2), (-1; 2; -2). Trang 21 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz x=l+mt x=1-t' Cau 177. Trong khéng gian hé toa dé Oxyz cho 2 dudng thang, d:sy=t d':}y=24+2t' g=-1+2t z=3-2t' duodng thang d cat d' khi: A.m=0. B. m=-1 C. m=1 D. m=2 Cau 178. Trong khéng gian hé toa dé Oxyz cho mat phang (P):x+ 3y+z+2=0 va duong x=l1t+t thang, d:)y=2-t .Trong cdc ménh dé sau, ménh dé nao ding? z=1+2t A.dc(P). B. d1(P) C. dcat (P) D. d//(P) Cau 179. Trong khéng gian hé toa dé Oxyz cho mat phang (P):2x+ y-z+3=0 va duong x=2+mt thang, d:\y=n+3t . Voi gid trinao cua m,n thi d nam trong (P) z=1-2t __5 m=-2 _5 m=--2 Ameo B42 ci 5 D479 n=6 n=6 n=-6 n=-6 2 Cau 180. Trong khéng gian Oxyz cho mat cau (s) (x -1) + (y+3) +(z +1y =3 va mat phang (P) 3x4 (m- 4)y- 3mz + 2m- 8 = 0. Véi gid tri nao cua m thi mat phang (P) tiép xuc voi mat cau (s ) A.m=-1. B. m=1 C.m=0 D.m=2 Cau 181. Trong khong gian hé toa dé Oxyz cho hai mat phang (a) : mex —y+(m -2)z+2 =0, (8) :2x+m>y-2241= 0. Mat phang (a) L (B) khi: A. || = 2 B. |m|=1 C. |r) = v2 D. |mm| = V3 Cau 182. Trong khéng gian v6i hé toa d6 Oxyztim ban kinh R ctia mat cau (s) biét rang, mat phang (Oxy) va mat phang (P) :z-2=0 cat mat Gu (s) theo giao tuyén 1a hai dong tron cd ban kinh [én hot 1a 2 va 8? A.R=9. B. R=2V65 C. R=3V35. D.R=4V61. Cau 183. Trong khéng gian voi hé toa dd dcho duong thang a, =(0;41). Diém nao sau day thudc duong thang d. A.M(2;-1;3). B.N(2;-1;-3). C.P(-2;1;3). D.M(2;-1;3). Cau 184. Cho diém M(-2; 5,0), hinh chiéu vuéng géc cua diém Mtrén truc Oy 1a diém A. M'(2; 5,0). B. M'(0;-5;0). Cc. M'(0;5;0). D. M'(-2;0;0). Cau 185. Trong khéng gian Oxyz, cho hai diém A(1;2;1),B(2;-1;2). Diém M trén truc Oxva cach déu hai diém A,B cé toa do la M 113 : B.M 1 O09 : CM 3.0.0 : D.M 0,4, : 2°2°2 2 2 2°2 Trang 22 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz B. Duong thang (d) khéng cat mat cau (5). C. Duong thang (d) cat mat cau (S) tai A (1;1;1). D. Duong thang (d) tiép xtic v6i_ mat cu (S) tai Bre 2). Cau 205. Trong khéng gian voi hé truc toa dé Oxyz, mat phang (P) :-4(x +1) +2(y—3)+2z=0 tiép xuic vi mat cAu (S):(x- 3) +(y-1) +(z+2) = 24 tai digém M, toa dd diém Mla: A. M,(-1;3;0). B. M,(1;3;0). Cc. M,(1;3;1). D. M,(1;3;2) Cau 206. Trong khong gian voi hé truc toa 6 Oxyz, cho mat cau (S):(x-1)? +(y-1f +(z-1) =17 va mat phang (P):2x+3y-2z-1=0. M la diém trén mat cau (S) sao cho khoang cach tty Mdén P dat gia tri lén nhat. Toa dé diém M1a: A. M(3;4;-1). B. M(1;3;0). C. M;3;1). D. M(-1;-2;3). Cau 207. Trong khéng gian voi hé truc toa d6 Oxyz, cho diém M(x; yz) thudc mat cau (S):x? ty? +2 -2x—dy-4z-7 =0. Toa dé diém M dé biéu thitc T =2x+3y+6z dat gid tri 1én nhat. A. u( 6, 3), B. m(-22:-2), C. M(1;2;6). D. M(-1;2;6). 7'°7'7 77° 7 Cau 208. Trong kh6éng gian voi hé truc toa d6 cho mat cau (S): x? +y +2? -2x+2z-2=0 va cdc diém A(0;1;1); B(1; 0;-3);C(-1;-2;-3).Tim toa d6 diém D trén mat cAu (S) sao cho tt dién ABCD “ thé tich 1én nhat ? 1 5 A.D(=; B. D(1;0;1). C.D Gr 3 73) ( ) Gi 3 “3 Cau 209. Trong khéng gian toa dé Oxyz, cho tam gidc ABC cd A(1;0;0),B(0;1;0), C(0;0;1). Toa d6 tric tam H cua tam giac ABC la: a(2,-2,-2), 3° 3° 3 111 1 .10¢1 A.H(1;1;1). an(Sa73: cul Ere]: Cau 210. Trong khéng gian voi hé toa dé Oxyz , cho cdc diém A(1;-1,0),B(0; 2;0),C(2;1;3) : Toa dé diém M théa man MA~ MB +MC =0 A. (3:2; -3). B. (3; -2;3). Cc. (3;-2; -3). D.(3;2;3). Cau 211. Trong khéng gian Oxyz, cho ba diém A(1; 0; 0),B(1;1; 0),C(0;1;1). Khi dé toa d6 diém D dé ABCD 1a hinh binh hanh: A.D(1;41). B.D(2;0;0). C.D(0;2;1). D.D(0;0;1). Cau 212. Trong khéng gian Oxyz, cho A(1;2;3) va B(-3;4;5).Toa dd diém M chia doan AB theo tisd k=2 la: A.M(5;0;1). B. M(-7;6;7). C.M(-5;10;13). D. M(-1;8;11). Cau 213. [Chuyén SP - Tan 2] Trong khéng gian vi hé toa d6 Oxyz, cho hai diém A(-1;2;3), B(3;-1;2). Diém M théa man MA.MA = 4MB.MB cé toa dé 1a. am(302). B.M(7;-4;1). Cc. u(ug 1 3). p.m(2:4:8). 3° 3 2’4 3°3°3 Cau 214. [Group toan 3K — fan 27] Trong khéng gian véi hé truc toa dé Oxyz, cho ba mat phang (P):2x-y+z+1=0, (Q):x-y+2z+3= 0 va (R):x+ y+1=0 va duong thang, 2). D.D(1;-1;0). Trang 25 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz AP Ae Goi d 1a giao tuyén cua hai mat phang (P), (Q)- Biét rang, d' la dung thang, vung gdc voi mat phang (R), cat ca hai duong thang dva A lanluot tai A, B. Duong thang d' di qua diém nao sau day? A.H(9;0;-6). B.L(7;1;-6) C.P(6;3;-5). D.K(5;-4;-5). Cau 215. Trong khéng gian voi hé truc toa d6 Oxyz, cho lang tru ding tam giac ABC.A'B'C' cé A(1,0;0), B(0;2;0), C(-1,0;0) va A'(1;0;3). Toa d6 trung diém M cia AB' la: 3 1 1,3 A.M} 0;0;= |. B.M| =;1;3 |. C.M| =;1;= |. D.M(1;2;3). 2 2 2°72 Cau 216. Trong khéng gian véi hé toa dé Oxyz, cho lang tru dimg tam gidc ABCA'B'C' cd A(1,0;0), B(0;2;0), c(-1, 0;0) va A\(L 0,3). Tim toa dé diém G’ 1a trong tam cua tam gidc A'B'C'. a.c(o3). Ba 0;2,1} C.G'(0;2;9). p.c (oa) 3 3 2 Cau 217. Trong khéng gian voi hé toa dé Oxyz, cho lang tru dimg tam gidc ABC.A'B'C' cd A(1,0;0), B(0;2;0), C(-1,0;0) va A'(1;0;3). Tim toa d6 diém D thudc canh AA' sao cho dién tich ADB'C’ bang 3. A.D(1;0;1). B.D(1;0;5). C.D(1,0;2). p.p{ 102), Cau 218. Trong khéng gian véi hé toa dé Oxyz, cho lang tru dtzng OAB.O'A'B' biét A(2; 0;0), B(0;4;0) va 0'(0;0;4). Goi I 1a trung diém cia BB'. Diém M trén canh AB, N trén canh O'A' sao cho MN 1 OI va MN = 2V5 .. Tim toa d6 trung diém cia MN. A.(1;1;0). B.(1;1;2). C.(1;2;1). D.(1;2;2). Cau 219. Viet phuong trinh duong thang A di qua M(1;0;-1) va tao voi mat phang (a):2x-y+3z-6=0 géclénnhat. x=1+2t x=1-2t x=1+2t x=2+t A. y=-t : B.4 y=-t : C.yy=-t : D.jy=-1 . z=-14+3t z=-14+3t z=-1-3t z=3-t Cau 220. Viét phuong trinh dudng thang A di qua M(4;-2;1), song song voi mat phang (a) :3x-4y+z-12=0 vacach A (-2; 5;0) mét khoang Ién nhat. x=1+4t x=4+t x=4-t x=4+t A. y=1-2t. B.4y=-2+t. C.jy=-24t. D.jy=-2-t. g=-lt+t z=1-t z=l1t+t g=-lt+t Cau 221. Viét phuong trinh dudng thang, A di qua A(L; 41) vuéng gdc voi duong thang, x=t A':sy=1+t vacdch diém B(2; 0;1) mét khoang én nhat. z=14+2t Trang 26 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz x=1-t x=14+t x=1+t x=1+t A.jy=l1+t. B.yy=1+t. C.jy=1-t. D.jy=1tt . z=l1+t z=1-t z=l1+t g=-lt+t Cau 222. Trong kh6ng gian véi hé toa d6 Oxyz viet phwrong trinh duong thang, A qua A (1 1,2) va vudng géc véi at = vee 5 dong thdi tao véi truc Oz géc lén nhat. x=l1 x=1-t x=ltt x=ltt A.y=l+t Bay=1. C. jy=1-2t D.jy=-2+t z=2-2t z=2+t Z=2 z=2t Cau 223. Trong kh6ng gian véi hé toa d6 Oxyz viet phuong trinh duong thang Aqua A (1 1,2), nam trong (a) ix+2y-z-1=0, déng thdi tao véi truc Oz géc nhé nhat. x=5+2t x=1+5t x=1+2t x=1+t Ay=2tt . B.ay=1+t . C. jy=1+5t. Dj y=142t z=l1t+t z=2+2t z=2+t z=2+5t Cau 224. Cho A(1,4;2),B (- . Viét phuong trinh dudng thang, qua A, Nien c&t dsao cho d(B,d) la nhé nhat. x=l+t x=1+t x=15+t x=1+15t Ady=4-t . B.jy=-1+4¢. C.fy=18+4t. = D.dy=4+188 z=2-3t zZ=-34+2t z=-19-2t z=2-19t Cau 225. Cho A(14;2),B(-1;2;4) 4-24-22 2, Viét phuong trinh dudng thang qua A, x=ltt x=ltt x=15+t x=1+15t A.y=4-t . B.jy=-1+4t. C.sy=18+4t . D.4 y= 4+ 18¢ z=2-3t z=-3+2t z=-19-2t z=2-19 Cau 226. Trong khéng gian véi hé toa dé Oxyz, cho 2 diém A(L 5 0),B (3; 3; 6) va duong thang, a APL A= Goi d la duong thang, qua B va cAt A tai digém C sao cho Sarge Gat gid tri nho nhat. x=1-4t x=1-2t x=-2+t x=1-3t Awy=-2t . Ba y=-3t . C.jy=3 : D.4 y =—4t z=2-3t z=2-A4t z=—4+2t z=2-2t Cau 227. Trong khéng gian voi hé toa dd Oxyz, goi (P) 1a mat phang song song véi mat phang (Oxz) va cAt mat au (x-1) +(y+2) +z? =12 theo duodng tron cé chu vi én nhat. Phuong trinh cua (P) 1a: A.x-2y+1=0. B. y-2=0. C.y+1=0. D.y+2=0. Cau 228. Trong khong gian voi hé toa d6 Oxyz, cho diém M(1;2;3). Goi mat phang (a) lamat phang chtta truc Oy va céch diém M mét khoang lén nhat. Phuong trinh mat phang (a) la: A.x+3z=0. B. x+2z=0. C.x-3z=0. D.x=0. Trang 27 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz 9°9'9 9’9'3 Cau 246. Cho mat phang (P) ix+y+z—-4=0.Tim diém Me (P) sao cho MA? +2MB* nho nhat, biét A(1;2;1), B(0;1;4). 2,102 B. M{ 0532 cM 4s;2 D.M(1;1;2). 999, A er 14 7%. 4i1 5), B. M 34:2), C.M(11;2). D. u($ 3°3 33) 33 Cau 247. Cho mat phing (P):x+y+z-4=0.Tim diém M ¢(P) sao cho |MA+3MB+2MC| nhé oh nhat, biét A(1;1;1), B(1;2;0), C(0;0;3). A.M(1,1,2). B. M 43,3 : CM 2. 3, 5 : D.M 34,3 : 2°2 3/3/3 3°92 Cau 248. Cho mat phang (P):x+y+2-4=0.Tim diém Me e(P) sao cho |MA+3MB +4Mc| nhd nhat, biét A(1;2;1), B(1;2;0), C(0;0;3). A.M(1,1,2). B. M{ 12,2 A). c. ul 2; ia). pm( Zia) 12/12’ 6'5" 6/12'12 x- = aytl_z-ll 2 -1 Cau 249. Trong khéng gian voi hé truc Oxyz, cho hai duong chéo nhau d, :—— , d,:~ +493 2-4 Tn aid khéng thudc d,vad, sao cho d(I,d,)+ suua) nho nhat. 7 2 3 A.1(5;2;5). B.1(7;3;9) C.1(7;-2;-11). D.1(-7;2;11). Cau 250. Trong khéng gian voi hé truc Oxyz, cho A(-1;3; 4), B(2;1;2) . Tim diém M sao cho biéu thie P = [MA +MB| dat gia tri nhé nhat. 2 2 Cau 251. Trong khéng = gian voi hé truc Oxyz, cho tam_ gidc ABCvoi A(2;0;-3);B(-1; -2; 4),C(2;-1,2). Tim diém E sao cho biéu thtrcP -|FA +EB +EC| dat gia tri nho nhat. A.D(1;4;1). B.D(1-1,1). C. D(-1;-2;-1). D.D(0;2;-3). Cau 252. Trong khéng gian voi hé truc Oxyz, cho 4 diém A(0;1;5);B (2; 0; 0);C (0; 0; 6),D(2; 4 -3) am(3:23] am 31-1), com(—$a}, D.M(-3;2;2). . Tim diéin E sao cho bidu thiscP =|EA + EB -CE—DE| dat gid tri nho nhat. az(ni] BE(0;-3:3] C.E(-1;-3;0) D.E(2; 0;-1) Cau 253. Trong khéng gian voi hé truc Oxyz, cho mat cau (s) : (x-3) +(y+2)" +(z-1) =100 va mat phang (P):2x- 2y-z+9=0. Tim I trén mat cau (S)sao cho khoang cach tir I dén (P)lon nhat. Ar=[22,-26,-7) prof 38) ¢ 7 2[ 22,267) pp i[-22, 26.7), 3 3° 3 “3373, 3°3' 3 3°33 Cau 254. Trong khong gian voi hé truc Oxyz, cho tam gidc ABC voi A(2;3;4);B (-2; -3; 0);C (2; 3; 0) -Goi 11a tam mat cau di qua 3 diém ABC cua tam giac. Tim I dé mat cau cé ban kinh nho nhat. Trang 30 | Nh6m Dé file word Nh6m Dé file word Chuyén dé Oxyz A.1(0;0;2) B.1(2;3;2) C.1(0;0; 0). D.1(-2;3;2). Cau 255. Trong khéng gian voi hé truc Oxyz, cho lang tru dtmg ABC.A’B’C’, voi a0.0a(osz0}c{9P.5.0:4(0.02) Tim toa d6 diém M thuéc canh AA’ sao cho dién tich tam gidc MC’D dat gia tri lén nhat, vdi D 1a trung diém ctia BB’. A. M(0;0;0) B. M(0; 0; 2) C.M(0;0;1). pal 00,3) Cau 256. Trong khéng gian voi hé truc Oxyz, cho mat cau (S):(x+1) +(y-4) +22 =8va diém A(3;0; 0); B(4;2;1). Tim gia tri nhé nhat cia biéu thiec P = MA + 2MB. A.maxP =2V2 B.maxP = 4V2 C.maxP = /2 D. maxP =3V2 Hét Trang 31 | Nh6m Dé file word Nhoém Dé file word Chay én dé Oxyz HUONG DAN GIAI Cau 1. Huéng dan giai: Chon A # Tur luan: Tir OA = ~i+ 3k > OA =(-1,0;3) => A(-1,0;3) ¢Tracnghiém: Cau 2. Huéng dan giai: Chon B ¢ Tu luan: Hinh chiéu cua diém M trén truc Ox 1a M, (-1; 0; 0) Cau 3. Huéng dan gidi: Chon D Tu luan: Ta co: OM =i-V3j+4k > M(1;4;-V3) Chiéu lén mp (Oxy) thi M'(1;4;0) Cau 4. * naa . , jJielty x=1 ¢ Tu luan: Ta co G la trong tam tam giac ABC thi {Te 5 y=- ¢ Tracnghiém: Cau5. Huéng dén gidi: Chon A Ty luan: Ta 6 AB =(-1;0;1),DC =(2-x;1- y;1-z) 2-x=-1 x=3 Tt giac ABCD 1a hinh binh hanh <= AB =DC @41-y=0 @sy=1=>D(3;1;0) l-z=1 z=0 @ Trac nghiém: Tinh toa dé véc to AB = (-1;0;1) .Ttr cac dap an tinh toa dé véc to DC duoc véc to nao bing véc to AB ta duoc dap an. Cau 6. Huéng dan giai: Chon A ¢ Tu luan: N nim trén truc x’Ox nén N(x; 0;0) => AN = (x- 2;1,-1); BN = (x- 3;2;1) N céch déu A va B: AN = BN y(x—2)? +141 = (x37 +441 © 2x=8Sx=4> N(4;0;0) @ Trac nghiém: Vi diém N nm trén truc x’Ox nén N(x; 0;0), ta loai dap an C va D Tir cac dap an con lai tinh AN va BN, dap an nao cho NA = NB ta chon. Cau 7. Huéng dan giai: Chon A. ¢ Tu luan: Vi M thuéc mat phang (Oxy) =>M(x;y;0) Trang 11 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz ene [ABC] Ta 06: d(A,BC)= =V13. BC BC ¢ Tracnghiém: Cau 20. Huéng dan giai: Chon c @ Tu luan: IA=IB Goi I(a,b,c) la tam dong tron ngoai tiép tam giac ABC. Ta cé: ) IA =IC > 1(2; 2; 2) : [ AB, AC | Al =0 ¢ Trac nghiém: C6 thé thir dap an bang cach tinh IA, IB IC va so snh Cau 21. Huéng dan giai: ChonD Tw luan: [a 3] = ||. sin a:b ¢Tracnghiém: Cau 22. Huéng dan giai: Chonc Tu luan: Ta o6: AB =(-1;0;1), AC =(1;4)1)> [ 4B, AC | =(-1;2;-1) ; _[48.ac]_ [aye +cayr _v6 2 2 2 ‘AABC ¢Tracnghiém: Cau 23. Huéng dan giai: Chon A @ Tu luan: Ta o6: AB =(-1;0;1),AC = (1;1;1) =[AB,AC]= (-1;2;-1), AD = (-3;1;-1) | 48,Ac |b Visep = =——=—= 1. ‘ 6 ¢ Tracnghiém: Cau 24. Huéng dan giai: Chonc @ Tu luan: Ta o6: Trang 41 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz D €Oy=>D(0;y;0). AB = (1;-1;2),AC = (0: -2;4) >| AB,AC |=(0;-4;-2), AD =(-2;y- 111) _[a,c].ap| Ac}? _/4y +2 Vazep = 6 » Vanco =50 [4y +2] Hand 6 y=8 _[48-AC] AD] [ay 9 “anep = Z . CALC cac dap an két qua nao thé tich ¢ Trac nghiém: Nhap_ V, bang 5 ta chon. Cau 25. Huéng dan giai: Chon A. @ Tu luan: Ta c6: AB =(-3;0;-4), AC =(4;0;-3) > [ AB, AC | = (0;-25;0), AD = (23-3) [ai.Ac]a0] a5 | _[ABAC] Vanco = aaBe = d(D,(ABC))= Manco — 3, AABC. ¢ Tracnghiém: Cau 26. Huéng dan giai: Chon D D €Oyz=D(0;y;z),z<0. d(D, Oxy)=1 |;|=16 ee D(0;y;-1). AB =(1;~1;~2),AC = (~4;2;2) >| AB,AC |=(2;6;~2),AD = (-2;y;-1) [ 48, AC] AD| oy -6 Y- 3 Vasey = [pac] ar 6 le yn 20 ley ey 237 D6i chiéu cac dap an ta chon dap an D. Cau 27. Huéng dan giai: Chon A Tu luan: D' Chon hé truc Oxyz nhu hinh vé. A(0;0;0), B(1;0;0), D(0;1;0), A’(0;0;1). B G ( ) | Ac,Dc'] ap| . d(AC,DC') === =—. [ 4c.0c' | V3 Trang 51 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Cau 28. Huéng dan giai: Chon A @ Tu luan: Chon hé truc Oxyz nhu hinh vé. [7eRo]a| , d(A'B,B'D) =—{ _—__ = ( ) [42.20 | v6 Cau 29. Huéng dan giai: Chon A Tu luan: x Chon hé truc Oxyz nhu hinh vé. A(0;0;0), B(3;0;0), C(0;4;0), D(0;0;4). 3 Suy ra: m(3:20], N(0;2;2), P(0;0;2). un {$012}, NP(0;-2;0). [ MN, NP |=(4;0;3). Suy ra (MNP) :4x+3z-6=0. Suy ra d(A,(MNP)) -%. Cau 30. Huéng dan giai: Chon A @ Tu luan: Chon hé truc Oxyz nhu hinh vé. Suy ra O(0;0;0), B(0;a;0), A(0;-a;0), C(2a;-a;0), D(0;0;a). Suy ra BC (2a;-2;0), BD(0;-a;a), nN [BC,BD |= (-2a7;-2n7;—2n") Suy ra (BCD):x+y+z-a=0. = 24 Be Cau 31. Huéng dan giai: Chon A. @ Tu luan: Chon hé truc Oxyz nhu hinh vé. Suy ra O(0;0;0), A(a;0;0), B(0;b;0), C(0;0;c). d(A,(BCD)) Trang 61 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Cau 39. Huéng dan giai: Chonc ¢Tu luan: Mat cau c6 tam I(1;0;-1), ban kinh R =2 d(L,(P))= 3>Rnén mat phang (P) va mat cau (S) khong cé diém chung. x=1+2t Goi d la duong thang qua I va vuéng goc voi (P) ,ad:y= —2t z=-l1+t giao diém cua d va (S ) la hai diém cé toa do Z, 41 , 144 . Vikhoang cach tir A 3.3 ~=3 33 3 dén (P)16n nhat nén A Z. 4,1 . 3.3 3 ¢ Trac nghiém:Thtr 4 phuong an thay diém co toa dd (3: 5 2) Khéng thudc mat cau (S)nén loai. 5 Khoa Ach tlre diém (1;0;-3) dén (P)la: = . oang cach tir diém (1;0;-3) dén (P)la 3 Khoang cach tir diém 74.1 dén (P)la: Bb 3.3 «3 3 AL 3 ; ole ola Khoang cach tir diém [- ) dén (P) la: ; : Cau 40. Huéng dan giai: Chon A ¢Tu luan: Mat cau ($)co tam 1(0;1;1) , ban kinh R=3 . Dé thay diém A nam trong mat cau nén mit phang (P)can tim di qua A va vudng géc voi IA. Do dé: (P):2x+z-6=0. Ban kinh dwong tron 1a: r= VR?-IA? = 9-5 =2. Cau 41. Huéng dan giai: Chon A ¢Tu luan: Mat cau dong kinh OA cé tam I(1;-3;2)la trung diém OA. Ban kinh R= is OA 2 ¢ Trac nghiém: Thtr toa d6 diém A va diém O vao cdc phuong trinh chi co ¥ A thoa man. Cau 42. Huéng dan giai: Chon B ¢Tu Luan: Gia str I(x;0;0) la tam cia mat cau. Vi mat cau di qua A,Bnén: Trang 91 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz IA=IB oo (x-1) +243 =(x-2) +27 ex=-3 Vay tam 1(-3;0;0) , ban kinh R=1A = 29 ¢Trac nghiém: Vi tam mat cau nam trén truc Oxnén loai A, C. Vi mat cau di qua A,B nén loai D. Cau 43. Huéng dan giai: Chon D 5 chee gas we ake pd . |2.24+1-2.3+10 ¢Tu luan:Khoang cach tir diém I dén mat phang (P) 1a: a(I,(P)) =.—__—— = 3 3 Ban kinh mat cau: R=¥47+3? =5 Vay phwong trinh mit cau 1a: (x- 2) +(y- 1y +(z- 3) =25. ¢ Trac nghiém: Do mat cau (Ss) c6 tam Inén loai AvaC. Lay mét diém M bat ki thuéc dtrong tron giao tuyén cua (P) va (S) . Kiémtra IM=4 . Cau 44. Huéng dan giai: Chon Ty luan:Mat cau ($) 06 tamI(1;-2;-3) , ban kinhR= 14 . Ta cé: d(I,(z)) =0<R nén (a) cat (S) theo mét durdng tron. Tam I(1;-2;-3) thudcmiat phing (a). ¢ Trac nghiém:Néu B dung thi A va D dung. Néu C dung thi B va D sai. Cau 45. Huong dan giai: Chon A Mat cau (S) co tam O(0;0;0) va ban kinh R= 22. Vi OM=1<R nén Mthuécmién trong cua mat cau (S).Goi A, B la giao diém cua dung thang véi mat cau. Goi H 1a chan dong cao ha ttr O cua tam giac OAB. Dat x= OH, tacd 0<x<OM=1, ding thdi HA = JR? OH? = 8-2 . Vay dién tich tam giac OAB la Soap = 50H. AB =OHHA=x8-%. Khao sat ham s6_ f(x) =aV8—27 trén (0;1], ta duoc max f(x)=f(1)=v7- Vay gia trilén nhat cia S44, = V7 , dat duoc khi x=1 hay H=M, noi cach khacla d1OM. Cau 46. Huong dan giai: Chon C Mat cau (S) 06 tam 1(1,-3;2) > IM = (6;2;3). Trang 101 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Mat phang can tim di qua diém M(7;-1;5) va cé vécto phap tuyén IM =(6;2;3) nén cd phuong trinh la: 6(x-7)+2(y+1)+3(z—-5)=0 © 6x +2y+3z-55=0. Cau 47. Huong dan giai: Chon B Dé (P) cat (S) theo giao tuyén 1a dong tron cé ban kinh Ién nhat thi (P) phai qua tam 1(1;—-2;1) ciia (S). Ta 06 Al =(1;-1;1), BI = (0;-3;2) >, =[AI,BI |=(1;-2;-3). Cau 48. Huong dan giai: Chon B _ |2+4+1-4] i. VE+P+E | Goi R 1a ban kinh mat cau, ta c6: R* =34+1=4 Ta cé: d(1,(P)) => (8):(x-2) +(y-4) +(z-1) =4. Cau 49. Huong dan giai: Chon A +) Goi H 1a trung diém cia AB, do tam giac IAB vuéng can tai I nén IH | AB va IA= V2IH +) d di qua M(2;1;-1) va cé vecto chi phirong us (2;1;-1). IM =(0; 2;-2) limiu| Jiertera => [IM;u] =(2;-4;-4) = d(I,d) = —= F 44441 Do dé IA= V2IH = V2a(I,d) = 2/2, suy ra mat cau cé phuong trinh (x-27 +(y+ DP +(z-1P =8. Chi ¥: Co thé tinh IH bang cach tim toa d6 diém H . Cau 50. Huong dan giai: Chon B Mat cau (S) c6 tam 1(3;3;4) va ban kinh R= 4>4d(1,(a)) = 2V3<R.Suy ramiat cau (S) cat mat phang (a) theo mét dung tron. Ta cé diém M < (a), IM= 14 <R nén diém M nam trong mat cau (S). Goi H 1a hinh chiéu vuéng goc cua I én (P)> H(1;1;2) Dé dwong thang A diqua M vanam trong (a) cdt mat cau Trang 111 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Nhap X-2Y+A+2 CALC Cau a:nhap -1= -1= —1= may hién 2 nén cau A sai Cau b:nhap -1= 1= —1= may hién —2 nén cau B sai Cau d:nhap -1= -1= 1= may hién 4 nén cau D sai Do do loai hét A,B,D ta chon cau C. Cau 55. Huong dan: Chon A Cach 1: SHb-L-tea sd _|f-2-2t+3|_ [t+] - _ |f-2-2t+7|_ [+5] Goi (t-L-t)e . Taco (1 (a)) = 3 a va (0 (0)) = 3 J Se Ne ye a 2 -t+1=-t+5 Do mat cau tiép xuic voi (a),(B) nén Isa) =4i wy eb ilapredes| 77 1-5 et=3 Suy ra 1(3;-1;-3), ban kinh R=d,. =2 CSE (H@)) 37 2 4 Phuong trinh mat cau can tim 1a: (x—- 3)" +(y+1) +(z+3) 0 Cach 2: thtr dap an Cau A. tim nhanh tam va ban kinh I(3;-1;-3),R= : : Ta thir I(3;-1,-3)ed [X+2¥+2A+3| [X+2¥+2A+7| V1+4+4 V1+444 may hién 0 nén cau A dung. Nhap vao may tinh bam CALC 3=-1=-3= Cau B:tam 1(0;1;0) ¢d nén loai cau B Cau C:tam 1(0;-1;0)ed [X+2¥+2A+3| [X+2¥+2A+7| V1+4+4 V1+444 Nhap vao may tinh bam CALC 0=-1=0= may hién = nén cau C sai. Trang 141 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Cau D: Tam I(-3;-1,3) ed [X+2¥+2A+3| [K+ 2v+2A+7| | V1+4+4 v1+4+4 Nhap vao may tinh am CALC -3=-1=3= may hién = nén cau D sai. Cau 56. Huong dan giai: chon cau A Ta c6 (ABC) ats ee 1 suy ra M(2;1,2) (ABC), goi H la hinh chiéu vuéng géc cia O lén a c M(2;1;2) (ABC). Ta céd OM =3 va ban kinh R= OH <OM suy ra ban kinh R cia mat cau lon nhat khi R=OM-= 3, xay rakhi H=>M Cau 57. Huéng dan giai: ChonD Tu luan: ¢Tracnghiém: -Loai A vi dé thay r°=4 ; - Loai B,C vi sai cong thttc. Cau 58. Huéng dan giai: Chon A —2a=-2 a=1 —2b=6 b=-3 ¢ Tut luan: Tir phuong trinh mat cau ta co: ° —2¢=-8 c=4 d=1 d=1 Toa d6 tam I(1; -3; 4). Ban kinh: r= V1+9+16-1=5 ¢Tracnghiém: - Loai D vi r<0; - Loai B,C vi sai cong thttc. Cau 59. Huéng dan giai: ChonB @ Tu luan: - Ban kinh mat cau 1a: r=d(I,(P))= Trang 151 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz ¢ Tracnghiém: - Loai A vi sai ban kinh; - Loai C,D vi sai cong thitc . Cau 60. Huéng dan giai: Chon A @ Tu luan: - Ban kinh mat cau la: r= AB= - Phuong trinh mat cu can tim cé dang: (x-1) +(y-2) +27 =14. @ Trac nghiém: Loai B,C,D vi sai céng thitc. Cau 61. Huéng dan giai: Chonc @ Tu luan: - Phuong trinh mat phang (P) qua I va vudng géc voi dong thang d co dang: x+3y+2z-7=0 - Toa dé giao diém cia mp(P) v6i (d) 1a: 1(3:3:0) - Ban kinh cua mat cau can tim la: r= I'= (2-0) “(3-4 +(0-2)° = ve - Phirong trinh mat cau can tim 1a: x? +( y-l) +(z- 2y = 2 @ Trac nghiém: Loai A,B,D vi sai céng thitc. Cau 62. Huong dan giai: ChonD @ Tu luan: Vi led nén I(t;0;-1) Vi mat cau (5S) tiép xtc voi mat phang (P) va (Q) nén ta cd: je+t+l] ret -5] aH) =4((0)) 9 eT aaa Khi do: 1(1,0;-1);r= 3 Tr © |2r+1|=|2r-S]eo r= Phuong trinh mat cau can tim 1a: (x-1)' + y? +(z+1)’ -2 ¢ Trac nghiém: : - Loai B,C vi sai ban kinh. Loai A vi sai cong thitc. Cau 63. Huéng dan giai: Chon D Tu luan: Trang 161 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz => 14 ~2a-2b+d =-2 31 b=— -2a-4c+d =-5 bo anne eS \4 se xreyeeetxe sty ya Be 0, Chon D. —4a-2c+d=-5 cw 7 7 7 7 2a+6c+d=-10 14 g-— 7 Trac nghiém: Thtr cac phuong an thda toa d6 bon diém A(1; 1; 0); B(1; 0; 2); C(2;0; 1), D(-1; 0; -3). Cau 71. Huéng dan giai: Chon B @ Tu luan: _ f-2.2-2-2) Taco: R=d(I,(a)) = 3.Do do chon B. ¢ Tracnghiém: Cau 72. Huéng dan giai: Chon B Tu Luan: Mat cau (S) cd: Tam /(1;-2;-1), ban kinh R=3. Suy ra mat phang (P) chita truc Ox vadi qua tam /(1;-2;-1). Do a6 chon B. Cau 73. ¢ Tw Luan: Mat phang song song va cach déu (P) va (Q) 1a (R): x+2y+2z+7=0. Huéng dan giai Ta 06: I1=d(\(R) => 1(3;-1,-3). Tw cdc phuong an va toa dé I, suy ra dap an D. ¢Tracnghiém: Cau 74. Huéng dan giai: Chon A Tw Luan: Mat cau (S) cd: Tam /(0;1;-1),cé hinh chiéu vudng géc lén d 1a K(2;0;0). Do trung diém H cua TT'nam trén IK va TH.IK =1 sali: 2. 3) Chon A. @Trac nghiém: Mat cau (S) cé: Tam /(0;1;—1),c6 hinh chiéu vudng goc lén d la K(2;0;0). Do trung diém H cla 77'n&m trén /K thir cdc phtrong an chon A. Trang 191 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz HUONG DAN GIAI VAN DE: “PHUONG TRINH MAT PHANG” Cau 75. Huéng dan giai: Chon B Tu luan: Dé bai cho toa d6 diém va vecto phap tuyén, thay vao cong thttc ta cé ngay dap sé. Phuong trinh mat phang (P):2(x—1)-(y+2)+3(z-0)=0< 2x-y+3z-4=0 ¢Tracnghiém: Dua vao veto phap tuyén loaingay dap an A. Thay toa d6 diém A vao cac dap an con lai ta chon duoc dap an B. Phan tich phurong an an nhiéu Nhiéu A. Thay nham vecto phap tuyén va diém. Nhiéu C, D thay sai cong thttc, hoac tinh toan sai. Cau 76. Huéng dan giai: Chonc ¢ Tu luan:Vi nhan biét hé s6 B= D=0 nén (P) chita truc Oy. Vay dap an Csai. Cac phuong an A,B,D dua ra dé hoc sinh cting c6 ki nang nhan biét cac yéu t6 cua phuong trinh mat phang. @Trac nghiém: Cau 77. (Chuyén KHTN)Trong khéng gian Oxyz, cho ba diém A(1; -2;-1),B (1; 0; 2),C (0; 2 1) : Mat phang di qua diém A va vudng géc voi dudng thang BC co phuong trinh 1a: A.x-2y+z+4=0. B.x-2y-z+4=0. C.x-2y-z-6=0. D.x-2y+z-4=0. Huéng dan giai: ChonD @ Tu luan: Mat phang can tim di qua diém A(1,-2;-1) va cé vecto phap tuyén BC= (-1;2;-1) cé phuong trinh 1a: -(x-1)+2(y+2)-(z+1)=0< x-2y+z-4=0 ¢ Tracnghiém: Mat phang can tim nhanBC = (-1;2;-1) lam véc to phap tuyén nén loai B, C. Thtr toa d6 diém A vao phuong an A, D thay phuong an A khong théa man nén loai A. Cau 78. Huéng dan giai: Chon B ¢ Tu luan: Hé sé cua x, y, z trong phtrong trinh mat phang 1a toa d6 véc to phap tuyén. Vi vay chon B. ¢ Tracnghiém: Cau 79. Huong dan giai: Chon A ¢ Tw luan: Phuong trinh (nf —1)x+(m—ly+(nt +2m-—3)z+2017=0(1) 1a phitong trinh khi vécto phap tuyén n= (nt —1m-1,nt +2m- 3) +0. Mat khac, Trang 201 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz nt -1=0 n=(n0 -1m-1,ne +2m-3) =O0khi Jm-1=0 hay m=1.Do dé,m#1(1) la mét mat nt +2m-3=0 phang. @ Trac nghiém: Thay cac gia tri m= 1, m=3, m=~-1 vao (1) néu thay vé trai bang 0 thi loai gia tri do. Cau 80. Huong dan giai: Chon A Tu luan:R6 rang, mat phang x+2y+z-6=0 cé vécto phap tuyén la n= (1; 2;1) . @Trac nghiém: Dé loai cdc phuong an C va D, ta st dung chitc nang CALC thay cac gia tri x,y,z vao phuong trinh mat phang thi thay khac 0. Cau 81. Huéng dan giai: Chon A Tu luan: Mat phang (P) di qua trung diém 1(2;2;3) ca doan thang AB, cé vecto phap tuyén IB(1; 4;-1) . Suy ra phuong trinh mat phang (P) 1a: 1(x-2)+6(y—2)-1(z-3)=0<x+4y-z-7=0. ¢Tracnghiém: Kiém tra trung diém I thuéc mp, kiém tra vecto phap tuyén. Cau 82. Huéng dan giai: Chon A Tur luan:Ta cd, mat phang (P) vudng géc dirong thang d nén mat phang (P) cé vecto phap tuyén n(1;2;-1). Mat phang (P) di qua diém A(1;1;-1). Vay phuong trinh mat phang (P) la: AU(x-1)+2(y-1)-1(z+1)=0<>x4+2y-z-4=0. ¢Tracnghiém:Kiém tra diém di qua, kiém tra vecto phap tuyén cing phtrong véi vecto chi phtrong duéng thang d. Cau 83. Huéng dan giai: Chon A ¢ Tu luan:Mat phang di qua trung diém /(2;0;0)va cé VIPT 1a n=(1;0;1) co phuong trinh la;x+z-2=0 ¢ Tracnghiém: Tht VTPT loai B,C.Thtr qua diém I loai D Cau 84. Huéng dan giai: Chon B ¢ Ty luan:Mat phang (P) di qua A(10;-1) va cé VIPT 1a n=(14:-2) cd phwong trinh 1a x+y—2z-3=0 @ Trac nghiém: Tht VTPT loai B,D. Tht qua diém A loai C. Cau 85. Huéng dan giai: Chon A Trang 211 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz phuong trinh (a):4x-z+1=0. @ Trac nghiém: Sir dung Mode-8 dua vé ché dé Vecto, nhap_ cdc vecto MN = (-1; 4-4),j= (0; 1,0)va tinh tich co hudng dé tim nhanh vecto phap tuyén. Cau 92. Huong dan giai: ChonA @ Ty luan:Goi A(a; 0; 0), B(0;b; 0), C(0;0;c). Ta cé G la trong tam cua tam giac ABC nén a2 ‘ a=6 l=- >jb=3. 3 c c=-9 ~3=5 3 Do Mat phang (P) 1a phwong trinh doan chan nén (P) ate 1. a c a x YY Z Vay, (P):e 45-5 = Le ax4 Oy 2218-0. @ Trac nghiém: Str dung phwong trinh mat phang o ting dap an, tim giao diém cua cac truc toa dé. Tir dé, tim duoc trong tam tam gidc néu tring véi diém G dé bai cho thi chinh la mat phang can tim. Cau 93. Huéng dan giai: ChonB Tu luan: Mat phang (P) di qua hai diém A, B va vung géc mat phang (Q) nén hai vector AB (2; 2; 1),n@) =(1;2;-1) c6 gid song song hoc chita trong mat phang (P). Suy ra vecto phap tuyén cia mat phang (P) 1a 11) = [ AB, no) |= (-4;3;2) . Vay phwong trinh mat phang (P) 1a: —4(x-0)+3(y—1)+2(z-0) <= 4x—-3y—2z+3=0. ¢Tracnghiém: Cach 1: Giai nhu tu luan. Cach 2: Thé nguroc tte dap an. Chon phuong trinh trong bén dap an di qua A, B réi kiém tra xem vecto phap tuyén cua mat phang do va mat phang (Q) cd vuéng géc hay khong? Néu vudng géc thi dap an do diroc chon. Cau 94. Huéng dan giai: Chonc Tu luan: Trang 241 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Mat phang (P) vudng géc voi hai mat phang (Q) va (R) nén hai vecton() = (3; -2; 2),12) = (5; -4; 3) co gia song song hodc nam trong mat phang (P). Suy ra vecto phap tuyén ctia (P) 1a ne) = [ m0), | =(2:4;-2). Mat khac mat phang (P) di qua diém M(3; -1 -5), nén phwong trinh mat phang (P) 1a: 2(x-3)+1(y+1)-2(z+5)=0< 2x+y-2z-15=0. ¢Tracnghiém: Cach 1: Giai ging tu luan. Cach 2: Thé ngurgc loai trtr dap an. - Thé diém M vao 4 phurong trinh 6 dap an, réi chon phuong trinh qua M. Kiém tra xem vecto phap tuyén cia mat phang 46 cé vudng géc vdi vecto phap tuyén ctia mat phang (Q) va (R) hay khong.Suy ra két qua. Cau 95. Huéng dan giai: Chon A + Ty luan:Mat phang (P)di qua A(1;0;1) va c6 VIPT 1a n=, Ary = (-3;2;-1) —3x+2y-z+4=0. @ Trac nghiém: Tht qua diém A loai B va D.Thit VTPT loai C. Cau 96. Huéng dan giai: Chon A ¢ Ty Ivan: LayB(-1-1,0)€(P)7(Q).Mat phangdi qua A va cd VTPT lan= ABA (1, An) =(-3;-1;7) ¢6 phwtong trinhla-3x—y+7z—-4=0. ¢ Tracnghiém: Thtr qua diém A loai B va C.Thtr qua diém B loai D Cau 97. Huéng dan giai: Chon A Tu luan: (Q):x-3y+2z-1=0 6 VIPT n, =(1;-3;2) (R):2x+y—z-1=0 c6 VIPT ny = (2;1;-1) Vi (P)vuéng géc voi hai mat phang (Q): x-3y+2z-1=0, (R):2x+y-z-1=Onén (P)cé VIPT la ny = [ng,m, |= (1;5;7) Ma (P) di qua diém M(-2;3;1) nén (P) co phuong trinh la (P): x+5y+7z-20=0 ¢Tracnghiém: Thay toa d6 M(-2;3;1)vao cac phurong trinh mat phang thi chi co dap an A thoa. Cau 98. Huéng dan giai: Chon A. Tu luan: Cach 1: (a): x+5y+9z-13=0 cd VIPT Ne) =(1;5;9). Trang 251 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz (B):3x-y-5z+1=0 co VIPT 1p) =(2;1;-1). Goi Ala duéng thang giao tuyén ciia hai mat (@): x+ 5y+9z-13=0 va (B):3x-y-5z+1=0. thi A cé VTCP i, = Fey Fy | = (-16; 32;-16) = -16(1;-2;1) . y=3n(h Zo)ea. 2 22 3 3 (P) di qua M(0;2;1)vacé VTPT 1a Fp) = [a,,.MN |= (23-3)- $(t:4:1)nén co phuong trinh 1a Cho z= 0-x=5 x+y+z-3=0 Cach 2: Phuong trinh chim mat phang c6 dang: m(x+ 5y+9z-13)+n(3x-y-5z+1)= 0 Phuong trinh mp(P) di qua M(0;2;1) <> m(0+5.2+9.1-13)+n(3.0-2-5.1+1)=0<>m—n=0. Chon m= 1=>n=1. Phuong trinh mp(P) la: x+y+z-3=0. ¢Tracnghiém: Thay M(0;2;1) vao 4 phuong trinh ta thay chi cé dap an A, B théa Cho z=0=x=5,9 352(2,3:0)e4.Thay vao 2 dap an Ava thi chiA thoa. Cau 99. Huéng dan giai: Chonc ¢ Tu luan: Mat cau (S) cd tam I(1;-1;0) ban kinh R=1 Ban kinh duong tron giao tuyén r= a =(1,-1,0) 2 Goi Np = (a;,b;c),a° +b’ +c? #0 , phwrong trinh mat phang (P):ax+b(y+1)+ce(z-1)=0 ABn, =0 a=b a=b Ta cd d ~1¢e la~cl_—_ 1 @4/c=0 (Py Py Ieee V2 c-4a Chon a=1 suy ra phitong trinh mat phang la x+ y+1=0,x+y+4z-3=0. ¢Tracnghiém: Buoc 1, thay toa dé A, B vao cac dap an déu thoa man nén khong loai bo dap an nao Buc 2, tinh khoang cach tir tam mat cau dén bén dap dn, dap an nao cho khoang cach bang r ta chon dugc dap an C. Cau 100. Huéng dan giai: Chon c @ Tu luan: Goi vecto phap tuyén ciia (P) 1 = (a;b;c), a +b? +c? #0 (Q) c6 vecto phap tuyén Ny = (1;-2;2) (P) L(Q)>nng = 0<>a-2b+2c=0 (1), phuong trinh (P):a(x-1)+b(y+1)+e(z-3)=0 Trang 261 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Huéng dan giai: Chon A Tu luan: Do (8) // (a) nén (B) co phirong trinh 2x +2y-—z+D=0 (D#17). Mat cAu (S) co tam I(1; -2; 3), ban kinh R = 5. Duong tron cé chu vi 61 nén cé ban kinh r = 3. Khoang cach tir t6i(B) ah = VR? = 5° -3 = 4 , |21+2(-2)-3+D| D=-7 d6 Ht | 54+Di/= 23 2427 +(-1)7 D=17 Do Vay (B) co phuong trinh 2x+2y—z—7=0. ¢Tracnghiém: Cau 106. Huéng dan giai: ChonB Tu luan: Phuong trinh mp (P) cé dang: xy Fla vi Me(P) nén ttt leobee be 2 be 2 be 2 Ta cé AB(-2;b;0), AC(-2;0;c). Khi dé, dién tich tam gidc ABC 1a $= f¥ +c? +(b+c) - Vib? +c? > 2be; (b+ cy > 4benén S > Jobe . Ma be = 2(b+c) = 4Vbc > be = 16. Do 4d $= V96 x yz Dau "=" xay ra <b =c = 4. Vay phuong trinh (ABC) la: tat gs he erty te 250. ¢Tracnghiém: Cau 107. Huéng dan giai: Chon A ¢ Tu luan:Goi (P) c6é dang ax + by+cz+1= 0( Truong hopd = 0 loai ) 1 a=-— 2b+1=0 4 Ta co hé phuong trinh :4—-2c+1=0 24b= -+ la+b+c+1\=|a+b+]| ot 2 ¢ Trac nghiém: Thir qua diémA vaB loai phuong dn C va D. Tht khoang cach loai phuong én B. Cau 108. Huéng dan giai: Chon A ¢ Tu luan:Ta c6 I 1a trung diém BC nénI [3 0; ;) Vay mp (Q) qua diém A va cé VTPT 1a n=IA An, =(5;10-6) suy ra dap an A. ¢ Tracnghiém: Kiém tra qua diémA loai phuong anD kiém tra vuéng goc mp (P) loai phuong anC Kiém tra catBC tai trung diém loaiB Cau 109. Huéng dan giai: ChonD @ Tu luan: Trang 291 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz if d H d [ Z/ sca Goi H la hinh chiéu vuéng géc cua A trén d Goi K la hinh chiéu vuéng géc cua H lén (P) =d(d;(P))=d(H;(P))=HK. Tacé HA>HK= HK lon nhat khiK=A. Ta tim toa dé diém H. x=l1+t Phuong trinh dwong thang d:{|y=1-t . z=1+t Hed=H(1+t;1-t;1+t) ; AH =(t-1;2-t;t+3) Ta 06: AH Lua = (1;-1;1) AH aa = 065 t-1-24t+1+3=06 = 0 AH =(-1;2;3) Vay phuong trinh mat phang (P):—1(x-2)+2(y+1)+3(z+2)=0< —x+ 2y+3z+10=0 Kiém tra su vuéng géc voi cdc dap an A,B,C,D ta thay chi cd dap an D thoa. ¢ Tracnghiém: Dung cach dap an kiém tra théa gia thiét. Cau 110. Huéng dan giai: Chonc Tu luan: t+y-3z+1=0 Xét hé phuong trinh: wry 2x+ 3y+z-1=0 *Cho z=1>x=6,y=4>A(6;-4,De(P)A(Q). *Cho z=0>x=-4,y=3=>B(-4;3;0)e(P)A(Q). Ta c6: n=(1;2;4) 1a VIPT ctia(R) Vi (T) di qua A nén phuong trinh ctia (T) cd dang: a(x-6)+b(y+4)+c(z-1)=0 (a+b? +c? #0) Do Be(T) nén ta cé: c=-10a+7b. Suy ra v= (a;b;-10a+7b) la VTPT cua (T) |-39a+ 30b| Vaio? +b a 102)" 5392+ 30bf Suy ra cos = in = v679 ” i +b +(7b-10a)" Tes Nén theo gia thiét ta co: cos = Trang 301 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz = V97139a— 30b| = 23) 3(1010? + 50b? — 140ab) <= 3.97(13a—10b) = 237 (101n — 140ab + 506?) © 850 + 32ab- 530? =0< a=-b,a= =o ea=-bta chon b=-1=a=1,c =-17. Phuong trinh (T):x-y-17z+7=0 e a= bta chon b= 85=>a=53,c=65. Phuong trinh (T):53x+ 85y +65z-43=0. ¢Tracnghiém: Ding cach dap an kiém tra théa gia thiét. PHUONG TRINH DUONG THANG HUONG DAN GIAI Cau 111. Huéng dan giai: Chon A Tu luan: Duong thang d di qua hai diém A(1;-1;2) va B(-3;2;1) c6 vector chi phuong AB= (-4;3;-1) hay u=(4;-3;1) x=14+4t Phuong trinh dwong thang d: /y =-1-3t Z=2+t ¢Tracnghiém: loai trtr B,D vi khong thay diém di qua 1a A(1;-1,2), B(-3;2;1) Con dap an A, C, ta thay toa dé diém B(-3;2;1) va duwong thang x=1+4t -3=1+4t t=-1 y=-1-3t 4 2=-1-3t {t =—Isuy ra diém B thudc dirong thang nén chon A. Z=2+t 1=2+t t=-1 Cau 112. Huéng dan giai: ChonD Tu luan: Tir phuong trinh tham sé nhan thay uy, = (0; 4-1) hay 2u, = (0; 2;-2) @Trac nghiém: Tir phuong trinh tham s6 nhan thay uy, = (0; 1-1) nén loai dap an A,B,C chon dap an D. Cau 113. Huéng dan giai: Chon A @ Tu luan: Trang 311 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Thay diém H(-2;-2;3) khéng thudc (P) nén loai dap an A, Cau 117. Huéng dan giai: Chon A: Tu luan: evéc to chi phtrong ctia durong thang 1a AB = (2:13). ¢Tracnghiém: Cau 118. Huéng dan giai: Chon B Tu luan: . ¢Tracnghiém:. Cau 119. Huéng dan giai: Chonc @ Tu luan: véc to chi phtrong cia dong thang 1a BC = (-1;-6;3) ¢ Tracnghiém: Cau 120. Huéng dan giai: Chon B @ Tu luan: Gia str d cat A tai M >M(2t; 1 +t; 3t) Ta 06: BM = (2t — 1;t —1;3t + 3) AB = (0;0;1) Goi H 1a hinh chiéu cua A trén A. Khi dé: d(A; A) = AH = AB =>4(4; A) na, = AB khi B = HEM | AB @BM.AB = 063t+3=0>t=—15M(—2;0;-3) 5 x = 1-3t Phuong trinh duong thang d la: jy = 2—2t z= -3 Cau 121. Huéng dan giai: Chonc @ Tu luan: Ta 06 tz = — =. [a7] = (4:4; 1) Goi (P) 1a m&t phang chtra d va di, ta tim duoc phirong trinh mat phang (P) la: x+4y—5z+23=0 Goi N 1a giao diém cua (P) va d2 => N = (46/39; -29/13; 119/39) Duong thang d can tim di qua N va cé vector chi phtrong uz => PTDT d 1a: Trang 341 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz 4629s * 39° *" 43° 7 39 =a =46/39, c= 119/39 => a+ c= 55/13 ¢ Tracnghiém: Cau 122. Huéng dan giai: Chon D @ Tu luan: Gia st) He d, , Ked, Jan lot 1a chan duong vuéng goc chung Khi dé H(1+3k;-1+ 2k;2— 2k), K(4+21;44 2t;-3-1) t=-l1> H(4;1;0) Vi AK Lu,;HK Lu, tatim duoc ' ° k=1= K(2;2;-2) x=44+2t Vay phurong trinh dt phai tim la j y=1-1 z=2t Cau 123. Chon A x=t-—2 Duong thang “Woe = M —2;3;1 €d vacé VICP u= 43;1 z=1+t Cau 124. Huong dan giai: @ Tu luan: Duong thang d di qua hai diém A,B cé VICP: u— AB— 2;-3;4 . x=14 2t PTTS cua d:jy=2—3t zZ=—3+4t @ Trac nghiém: Nhan thay d co VTCP la: u—AB= 2;—-3;4 . Ta loai hai dap an A,B Con lai hai dap an C,D chicd D théa vi duéng thang d di qua diém A 1;2;-3 . Cau 125. @ Tu luan: AL a Su, =n, = 2;-3:5 A qua M 2,0;—3 x-2 y 243 uy = 2;-3;5 2 3 5 Trang 351 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz ¢ Trac nghiém: AL a >u, =n, = 2;—-3;5 . Ta loai duoc hai dap an A,D. Con lai hai dap an B,C chicd C thoa vi dong thang A di qua diém M 2;0;-3 Cau 126. @ Tu luan: Vi d song song voi P vavudng goc voi A nén d c6 VTCP la: U4, =|Mp; A = -5;2;4 B 2;-1;5 €d _ _ d: = prep: 22 =¥ tt 2-5 ‘|VTCP :u, = —5;2;4 5 (2 4 ¢ Tracnghiém: Vi d song song véi P vavudng gocvoi A nén d co VICP la: u, L nit, — u,nén ta lay VTCP ctia cdc dung thang phia duréi dap an [an hrot nhan v6 hong voi np va uy, xem cé bang 0 hay khéng. Nhu vay ta loai diroc hai dap 4n C,D con lai hai dap an A,B chon A viduong thang d diqua B 2;-1;5 Cau 127. x = 2t d, :}y=11t,Goi B=And, +B 2t;1+1;t z=t uy = MB = 2t;t;t-1 Do Ald uu, =O 2;t;t-1. 14-0 =04=0 =u, = 0;0;-1 M 0:41 x=0 A:)— SsA:jy=1 u, = 0;0;-1 2—1-t Cau 128. Goi H 1a hinh chiéu cui B lén dung thang d. Ta cé: d B;d =BH < AB. Vay d Bd mmx &BH=ABSH=ASABld Duong thang d song song voi P vavuéng gocvéi AB nén co VTCP: u, =|n,;AB| = 11-1 PrcT cua d:2 ata ¥at_ 271 1 1 1 Cau 129. Huong dan giai Chon Trang 361 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Cau 138. HUONG DAN GIAI Cing c6 vecto chi phirong 1a w= (1;1;1) Cau 139. HUONG DAN GIAI Vecto chi phuong w= MN = (—1;1;-2) Cau 140. HUONG DAN GIAI Vecto chi phuong U= Na = (1;3;-1), diém di qua M (2,-3.1) Cau 141. HUONG DAN GIAI Vecto phap tuyén cia (P) 19 2” = b-2:)) Vecto phap tuyén cata (2) 1a "= (b-D Vecto chi phuong u= [npsno |= (1;3;5), diém di qua M (0;-1;0) Cau 142. (Dé suu tam va bién tap) HUONG DAN GIAI Goi B 1a giao diém cuia dong thang A va truc Ox. Khid6 B(b; 0; 0). Vi A vudng géc voi duong thangd nén AB Lu, (voi AB=(b—1;-2;-3),u, = (251-2) Suy ra ABu, =0<>b=-1.Do d6 AB = (-2;-2;-3). x-1 Chon VTCP cho dong thang A 1a uw, =(2;2;3). Phuong trinh A 1a = a3 “3 HUONG DAN GIAI Cau 143. Dap an: D Cach 1: Ta cé mat phang (P) cé vécto phap tuyén 1a "py = (2m-1 3;-m — 1) va mat phang (@) cé véc to phap tuyén la m9) = (1:1;-1) => [ron | = (m —2m—-—2:2m—- 4) P) Theo gia thuyét: (P) song song (2) suy Ta 1%) cing phuong voi Trang 391 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Thit lai, ta cO (P) 30+ 8y-324+3=0@rt+y-z4+1=0 Suy ra (P) tring voi (Q). Vay khéng tén taisé m théa m&n yéu cau bai todn. Cach 2: Theo gia thuyét (P) song song (@) nén ~ = i a # ae e fr - Vay kh6ng t6n tai sé m thoa man yéu cau bai todn. Cau 144. Dap an: A Cach 1: d 1a giao tuyén cua hai mat phang (P) va (@) nén d cé co phutong trinh thoa man 3r+4y-22-1-0 |7 1+ ae . : $y 422-3=0 Syy= SY suy ta d cé vécto chi phurong lau = (6;-4;1). z=lt+ ) = (3:4;-2) va mat phang (@) cé No) Cach 2: Mat phang (P) cé vécto phap tuyén "p = (1 2:2) d la giao tuyén cua hai mat phang (P) va (2) nén d 6 vécto chi phwong la UW) = [ma | = (12;-8:2) Cung phuong vi u= (6;-4;1). Cau 145. Dap an: B A di qua diém A(L 1-1) cé vécto chi phuong 1a au = (1,-2:2) va d diqua diém A(L-11) cé vécto chi phuong 1a u, = (2 2:1) 2+2.1=0cu, Lu, suyra A vudng goc voi d Mat khac | u,:u, |= (6:36), AB =(0:-2.2) >| u.-u, | AB=-60+3(-2)+62=6+0 Suy ra A va d chéonhau. Cau 146. Dap an: B Cach 1: A di qua diém A(1:m;n) cé vécto chi phuong la uy = (-2:2:1) va d di qua diém B(I, 3.6) 6 vécto chi phuong 1a u, = (6;-6:-3). Ta co [us | = (0;0;0) suy ra u, cling phuwong voi u, . Vay dwong thang A va d tring nhau khi va chi khi A(tm;n) nam trén d 1=1+6t t=0 Do dé d: {m= 3-6t@\m=3.Suyra Kam +n =6+3 =45. n=6-3t n=6 ewan ~2_ 2 1 oo. so Cach 2: Vi — = 3°73 nén u, cling phirong voi wu, Vay dudng thang A va d tring nhau khi va chi khi A(1:m;n) nam trén A Trang 401 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz 1-1_3-m_6-n {re Do d6 —— = —— =—— & _ n=6 Suyra Kam +n? =6 +3 =45. Cau 147. Dap an: B (S) cd tam 7(2;3:1), ban kinh R= 2? +3°+1?+2=4 va (8) c6 tam 1/(3:13), ban kinh Ro =V3 +P 4+3°+30=7. Tao If! = (1:-2:2) > W/ = JP +(-2) +2 = 3. Suyra I! =R/-R Vay (S) tiép xuc trong voi (s’). Cau 148. Dap an: C Cach 1: ($) cd tam I(1;2;0), ban kinh R= v1’ +2 +0? -1=2 va (8!) c6 tam 1’ (2;4:2), ban kinh B= [P+ +2 —(m+15) = VO—m(m<9). Ta c6 II! = (1:2;2) > / = VP +242 =3.Suy ra (8) khong cé diém chung voi ($’) khi va chi khi / > R+ Ri 3>24+V9-m oV9-m<109-m<lom>ss. Cach 2: Chon m=0,tacé R' =3=R+R’ > II’ loaidap an AvaD Chon m=-9,tacd R/ = 3V2 > R+R! > 11! loai dap an B Vay ta chon dap an C. Cau 149, Dap an: B _[20+20+10+6|_, P42 eP Theo gia thuyét mat phang (P) cat mat cau 3) theo giao tuyén la mot dong tron co ban kinh (S) c6 tam 1(0,0;0), ban kinh R= Vk . Ta 06 d(I;(P)) bang r=3 nén R= J(a(1,(P))) tr =J24F =J13 > Vk=VB => k=13. Cau 150. Dap an: A @ Tu luan: e (P) co vtpt n,=(0;3;-1) va (Q) cd vtpt n, =(3;3;-2) nén d' cd mét vt la Pr Mp Pt MN cp tip =~ 3 [tiitig |= (11:3). ¢ Taco vtep cua d la ii, =(2;1;-1) va i,i,=O0 néndild'. ¢ Tt phuong trinh (P) va (Q), cho y=0, suy ra x=1 va z=7. x=lt+u Duong thang d' co ptts 1a y=u Z=-7+3u Trang 411 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz x=1+t y=t : et=1sI 2;11 .Suyra M=241+1=4. zZ=-1+4+2t 2x+2y—z—-5=0 ¢ Tracnghiém: Cau 159. Dap an: B @ Tu luan: Tacd: S céotamI 2;1;1 ;bankinh R=2 dl: P _|224+21-l+m| _[3+m PP — ecu Dp ai , op BHM . Dé S va P giaonhau thi d I; P SRe— <2 +nls6 <-6<34m<66-9<m<3 ¢ Tracnghiém: Cau 160. Dap an: A @ Tu luan: Ta xét tirng ménh dé mét Xét ménh dé A ta thay khithay A 1;1;0 vao P ta duoc:2.1+1—-0+3=0 thoa man Mat khac ta 6:5 = = => => => P //Q .Vayménh dé A dung. Ta khong can xét dén cac ménh dé con lai. ¢ Tracnghiém: Cau 161. Dap an: A @ Tu luan: S$ ity —2 —2x+4y—22-8=0 c6 tam I 1;-2;1, ban kinh R= V4 2143-2 +11-11] Taco d I; P =~—-——————__ = = R.. Vay P _ va S tiép xucnhau. V2424+2 v4 Cau 162. Dap an: B Tu luan: ¢Tacé A qua M —2;2;-3 c6VTCP a= 2;3;2 AM, al i V49--4+100 __ 53 al 44944 17 3 = AM= —2;2;-1 =|4M,q|= -7;-2;10 +d A;A = Ké BH LA, tacé BH ="Cu4 Xét AAHB c6é R? =16+9=25 Vay phuong trinh mat cau S : x7 +y*>+ z+2°=25. Trang 441 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz ¢Tracnghiém: Cau 163. Dap an: A @ Tu luan: m-1_ 2 _-3_-7 m-1=3 m=4 Ta co khi ——=——~=—4#—© e : ace (@)//(8) , -6 n+l 6 3 es fess ¢ Trac nghiém: Cé thé thay gia tri cu thé vao dé thtr chon. Cau 164. Dap an: A @ Tu luan: Dé (a) vudng gocvoi(Z) thi Int — mt —2( nt -2)=0< nt =4|mj=2 ¢ Trac nghiém: Str dung may tinh nhap biéu thtre 2X? — X? - 2(X? - 2) =0,,sau dé dung CALC dé thir chon cac dap an. Cau 165. Dap an: A ¢ Tw luan: Duong thang d, vecto chi phtrong u,(2;-1;1) : Goi M(1-#;1+2t;-1+t) 1a giao diém cua duong thang A va d, . Khi do ta cd AM(-t;-1+ 2t;-4+t) la mot vec to chi phuong cia dong thang d, . Vi d, vudng goc voi d, tacd 4AM =0< 2(-t)+(-1)(-1+.2)+1(-4+#)=08=-1 Do dé AM(1;-3;-8) 1a mét vec to chi phttong ctia duong thang A . Vay phuong trinh dwong thang A: — = = = = ¢ Tracnghiém: Vi tat ca cdc dong thang trong phuong an déu di qua diém A do dé ta chi cn kiém tra diéu kién vuéng géc. Tich vé huéng cia hai vec to chi phuong bang 0 1a chon. Dé thay 2.14 (-1)(-3)+1.(-5) =0 nén phitong an dung la A. Cau 166. Dap an: C ¢ Tw luan: Duong thang d, di qua M,(1,0;-1) cé vec to chi phuong u, (2;1;1) Duong thang d, diqua M,(-1;0;3) 06 vec to chi phuong u, (-1;0;2) Ta cé: uy, = 0; [ mm, |= (2;-5;1) va MM, (-2;0;4) Suy ra | u,,u, |.M\M, = 2.(-2)+(-5)0+14=0, Vay d, cat va vuéng gécvdi d,. ¢ Trac nghiém: Nhan thay phuong an A va phtong an D 1a hai phat biéu trong duong nén loai . Mat khac UM, =0 nén phutong an dung la phuong an C. Cau 167. Dap an: A ¢ Ty luan: Ta cé mat cau (5) cé tam 1(1; 2,3) va ban kinh bang 2 . Trang 451 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Vi dung tron giao tuyén cling cd ban kinh bang 2 nén m&t phang (P) di qua tam I cua mat cau. Do m&t phang (P) chtta truc Ox nén cé phuong trinh dang By+Cz=0 Ta c6 1(1;2;3)e(P)=>2B+3C=0 ; chon B=3 thiC=-2. Vay phwong trinh m&t phang (P):3y-2z=0 . @ Trac nghiém: Phat hién duoc mat phang (P) can tim di qua tam ctia mat cau (s) . Do dé chi cn thtr chon mat phang nao di qua I (1;2;3) thi théa man. Cau 168. Dap an: D ¢ Ty luan: Ta cé mat cau (5) cé tam 1(-1,2; 1) va tiép xuic voi mat phang (P) nén cé ban kinh _ [2-24 21-7] 3. Cau 169. Dap an: C Ta cé mat cau (5) cé tam I(1;1;-2) va ban kinh bang R=2. Goi r,;4;r, Tan lvot 1a ban kinh dung tron (C,), (C,), (C,)va h,;h,;h, Yan lwot 1a khoang cach tir tam 7 dén ba mat phang chita ba dung tron (C,), (C,), (C,). Khidétacd 1? +92 413 = Rh? +R? — 1} +R? —h} = 3R? (hp +h} +h}) . Viba mat phang di qua A déimét vuéng gécnén h? +13 +h} =1A* =1 Vay tong dién tich cia ba hinh tron (C,), (C,), (C,)la a(r2 +173 +12) =9(3R? -1A?) = 2 (3.4-1)= 110 Cau 170. Dap an: A ¢ Tu luan: Voi m=2 thi 2 mat phang cd phwong trinh 2x—2y+3z-6=0 va —2_ 3. -6 2x—2y+3z—10=0. Xét tilé $-$=3-s Hai mat phang song song. Cau 171. Dap an: A 2 ¢ Tw luan: Diéu kién hai mat phang song song: 2m _ 3 = = a4" n -6 -6 2 m 6 Cau 172. Dap an: A ¢ Tw luan: d, c6 vtep “= 2;3;1 ; d, cd vtep u, = 3;2;2 => u, va u, khong cling phuong > hai duong thang cat nhau hoac chéo nhau Trang 461 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Cau 181. Dap an: A Mat phang (c) 1 (8) khi 1.2) 240) = 0. 2? — nt -2(n? -2)=0 <> |m|=2. Cau 182. Dap an: B Goi 1(0;0;m) €Oz. Taco: R= jo I,, Oxy Tony R= find? +4 => R=@ 1,,P +7, R= yfn—2f +64 TIM TOA DO DIEM THOA MAN DIEU KIEN CHO TRUOC HUONG DAN GIAI =ne|4=m 2° | 6445m=165R=265. Cau 1. Huéng dan giai: Chonc ¢Tu luan: d di qua diém M (-2;1;3) Cau 2. Huong dan giai: Chon C ¢Ty luan: Voi M(a;b;c) => hinh chiéu vudng géc cia M lén truc Oy 1a M,(0;b;0) Cau 3. Huong dan giai: ¢Tw luan: M € Ox=> M (a;0;0) M céch déu hai diém A,B nén MA? = MB? & (1-a) +2 +P =(2-a) +2427 @2=3e0=5 Cau 4. Huong dan giai: Chon D ¢@ Tu luan: Cach 1: M (5+ 231+ 31;2-2r)ed; AM (24 2m;3 +3m;—-2— 2m) 2 =0 M (5;1,2 = AM =NiT (+m) =17 63)" >| ( ) m=— M (1;-5;6) Cach 2: Kiém tra cdc diém thudc dirong thang d cé 2 cap diém trong dap an B va C thudc durong thang d . Ding cong thitc tinh dé dai AM suy ra dap an C théa man. Cau 5. Huong dan giai: Chon C ¢ Phuong phap ty luan (Chuyén vinh [an 1) Ta cé phuong trinh mat phang (P) diqua M vudng gécvéi d la: 2(x-2)-1(y+3)+2(z-1)=0< 2x- y+2z-9=0 Trang 491 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Cau 6. Cau 7. Goi I 1a giao diém cua duéng thang d va mat phang (P), khidé toad6 J langhiém cia xt] yt2_ z hé} 200-1 2 =31(Is-3:2) 2x- y+2z-9=0 Goi M' déixting voi M qua d thi / la trung diém cha MM' => M'(0;-3;3). ¢Phuong phap trac nghiém Tim toa dé trung diém cla MM’ Kiém tra xem c6 thudc durong thang d khong Néu kh6ng thuéc ta loai, néu thuéc kiém tra thém MM ‘ua =0 thi diém dé thoa man. Huong dan giai: Chon A Chuyén Thai Binh Ian 3 Cach 1: Kiém tra cac dap an: Ta cd: M(-1; 0; 1)e(P). (P) co mét vécto phap tuyén n(1;1;1) AM (-1,—1;-1) > AM cing phitong voi n > AM L(P).Do dé M(-1; 0; 1) 1a hinh chiéu vudng géc cua A trén (P). Cach 2: Phuong phap tu luan: x=t Goi A 1a dwong thang di qua A va vuéng gocv6i (P). Tacéd (A):4 y=1+t z=24+t Toa d6 giao diém cua A va (P) 1a M(-1; 0; 1). Do dé M(-1; 0; 1) la hinh chiéu vuéng goccua A trén (P). Huéng dan gidi: Chon B Luong thé Vinh Ha Ndi lan 1 - Phuong phap: Hai vecto vudng géc vdi nhau thi tich v6 huéng cua ching bang 0. Néu H 1a hinh chiéu vuéng goéc cia diém M (khong nam trén dirong thang d) lén duong thang d thi vecto chi phwong cia duong thang d vuéng géc voi MH. - Cach giai: Tit phuong trinh tham sé cia duong thang d cé vecto chi phtong d 1a u(3;1;-2) ViH nam trén dwong thang d nén H(-1+3t;2+t;1-2t). Khi dé MH(-5+3t:1+t;-2t) ViH lahinh chiéu vung géc cla M én dnén MH.u=03(-5+3t)+1+t-2.(-2t)=0 Trang 501 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz © 14t-14=0 t=1.Khi dé H(2;3:-1) Cau 8. Huéng dan giai: Chon A ¢Tw luan: Thay Ian lot toa d6 diém A(1;1;5); B(;—2;2);C(1;2;3) vao phuong trinh mat cau (S) thay toa dé A,B théa man con C thi khéng théa man, chon A ¢Tracnghiém: Cau 9. Hing dn git Chom AM (10) u(232). M €d>M(1+ 2r-1-1;1) AABM vudng tai M => AM BM = 0.6 6° 41 = 069 1= Ohoke r= > Bs aes a 7-5-2 Vay cé hai diém M thoa man M (1;-10), u( 22). Cau 10. -Huéng dan gidi: Chon A M €d>M(14+t;2-1;14 21) low 7 7 T 1 ps “1 7 Sasna = 5 AB.AM |= —4((3r+7) +(3+5)' +(-4) = Sir #721490 = 5 f18(0-+2) +18 Yéu cau bai toan & Y18(142)° +18 bé nhat r= -2 Vay M (-1;4;-3)nén tung d6 diém M bang y,, = 4. Cau ll. — -Huéng dan gidi: ChonB Hed, d6 dai AH ngan nhat khi H 1a hinh chi€u cua A lén d. Taco H(2t; 1+4;2-1)va AHu, =0@t=0. Suy ra H(0; 1; 2). Dat f(y) =2x-yt+z+l. Tacd f(A).f(B) = (-6).(—-30) = 180 > Onén hai diém A, B nam cing Cau 12. Huong dan giai: phia so véi mat phang (P). Goi H lahinh chiéu cua A lén mat phang (P). Goi 4’ la diém déi xtmg cla Aqua mat phang (P). Khi dé hai diém A’, B nam khac phia so voi mat phang (P). Ta tim duoc H (1;2;-1) = A'(3:1;0). Tacé MA+ MB =MA'+ MB> A'B Suy ra MA+ MBnho nhat khi MA+ MB = MA'+ MB= A'B & A’, B, M thang hang hay M 1a giao diém ctia A'B va (P). x=3+t Ta c6 :(P):2x— y+z+1=0. vaA'B:4 y=1-t Suy ra M(2; 2-3) z=3t Vay S=at+b+c=l. Cau 13. Huong dan giai: Chon B Trang 511 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz MB | AB <> AB.BM =0< x+ y+3z-11=0 (2) AM = V61 > (x-1) +(y+1) +2? = 6103) Tur (1), (2), (3) suy ra: M(6;5;0), M (—2;-5;6). Cau 22. Huéng dan giai: Chon A ¢ Tu luan: Diém chung cua dwong thang va mat cau 1a nghiém ctia hé: x=1+2t yale (te®@)> = > A(t:1);:B-L;4;-2 ) z=14+2t . 1-8 ue" 99" 9 (x41)? + (y+ D? +(Z-2) =9 gs a 7.1.7 . ¢Trac nghiém: Thay toa dé cua A (1;1;1); BC Sig) vao phitong trinh mat cau thay thoa man nén chon A- Cau 23. Huong dan giai: Chon A x=1+2r ¢ Tu luan: Diong thang qua tam mat cau cd phuong trinh: }y=1+r giao cla dwong thang va z=1+2r x=342t t=-l mat phang (P):-4(x+1)+ 2%(y-3)+22=0 yp nghiém cia hé 3 —A(x+1)+ 2(y- 3)+ 2z=0 z=0 @ Trac nghiém: thay toa d6 tung diém thay M,;M, nam trén mat cau, va chi M, nam trén mat phang. Cau 24. Huong dan gidi: Chon A @ Tu luan: Goi M,(%i¥oiZ) 1a diém nam trén mat cau khi d6 (x, -1)%+(y)-)?+(q—D?=17 dM, «py = [2% +390 2% “HI | 2% “F389 =D= Azo“) +2 | | 2G =D +309 == AS =) 42 . vi7 vi7 vi7 d(My3P) < Loe + 300 =D = 20 D1+2 < V7 -D? + Oo =D? + =D? +2 19 vi7 vi7 vi7 2% — D+ 39 -)- AH —-) 20 Hol _ yl _ aol a dat duoc khi |} 9 3 2 (x) - IP + Op -D? + (@q—DP=17 ¢ Trac nghiém: Duong thang di qua tam mat cau vung goc voi mat phang P cat mat cau (S) tai hai diém phan biét 1a M(3;4;-1) va M(-1;-2;3) . Tinh khoang cach Ian lot ttr hai diém d6 dén mat phang thay M(3;4;-1) co khoang cach lon nhat, chon M(3;4;-1). Cau 25. Huéng dan giai: Chon A @ Tu luan: T= 2x+3y+ 6z = 2(x-1)+3(y — 2)+ 6(z—2)+ 20 | — 20] 0x 1) + (y— 2) + 6(2— 2) |< f49[(e-1)2+(y-2)2 (z-2)7) = 28 d(M,;P)max = -1 Trang 541 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz 15 x=_ (x1)? +(y-2)? +(c-2)?=16 7 |T-20|<28>-8<7<48 yay T= 48 | _, o y= 20 (15,8,38) ay “max 2° 3° «6 7 T7177 2x+3yt+6z=48 38 gee 7 ¢ Trac nghiém: Thay lan lot toa dé cdc diém trong cdc phuong an vao pt mat cau 2 2 2 1526 38 1.2. 10 2 mae. us (S):(x-D° + (y- 2) + (z- 2 =16 thay M PPT iM pp ; M (1;2;6).thoa man, tinh gia tri T= 2x+3y+6z tai bd ba gia tri trén thay Cau26. — Hudng dan gidi: Chon A @ Tu luan: Ts) = 48 nhan gia tri lén nhat nén chon A. Goi M(x; y;z) 1a diém nam trén mat cau khi d6 (S):(x-1)? + y? + (z+)? =4 mf (ABC) :2x-2y+z+1=0 1 Ss VABCD = 3 .d(D;(ABC)) nén Vigcp dat gia tri lon nhat khi d(D;(ABC))l6n nhat. a ABC x=1+2r Duong thang di qua tam mat cau va vudng gocvdi mat (ABC) 1a (d):} y=-2t za-l+t Giao diém cha (d) v6i mat cau langhiém cia hé x=14+2t y=-2t 14 °=5 7, 4,1 © D(-s:5;-5) Vv Dy(e3- 55-5 z=-l+t v6 3 ? G 3 > (x- 1)? + y? + (+I =4 Tinh khoang cach ttr D, c14,5) v p,d@;-4-4) dén mf (ABC) thay p44 théa man. Chon A 33 3 “3 3° 3 . “3 3 °3 ¢ Trac nghiém: Thay [an hrot cac diém trong cdc phitong én vao pt mat cau thay phuong an A,B.C théa man, tinh khoang cach tt cac diém trong cac phurong an A,B,C thay phuong an A thoa man khoang cach dén mf(ABC)16n nhat, chon A . Cau 27. Hung dan giai. Chon B Tu luan: . Tir gia thiét suy ra phuong trinh mat phang (ABC): ptitiel (PT mp theo doan chan). Goi H(xy5Yyi%4) thudc (ABC) => xy + yy +2, =1 (1) . . - . _ [AH.BC=0 . Do H la trirc tam tam giac ABC nén AH | BC,CH | AB nén:,__, (). CH.AB=0 Ta 6: AH =(xy—Lyy.24), BC =(0;-131) CH =(xpsyn.2H -1), AB =(-1;1;0) (xy eee Le +2 =0 © Xy = Vy = 2% = 1/3 Xy(-1)+ Yy.1+ (Zq —D.0=0 HOH “Ht Do do hé (*) =| Xp + Vy =O Trang 551 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Z x 111 ¢ Trac nghiém: dé thay ABC la tam giac déu = trirc tam cting chinh 1a trong tam > H (3: ; ] 3/33 Cau28. Huong ddn gidi: ChonB Tu luan: Xy =Xy—XyptXe =3 MA-MB+MC=06 Yu = Yaa Vet Vo =-2 ly = lap tee =3 Cau 29. Hung dan giai. Chon D. Tu luan: AB = (0; 10),DC = (-xp;1- Ypi1- Zp) Ti gidc ABCD 1a hinh binh hanh khi va chi khi_ AB = DC © D(0;0;1). ¢ Trac nghiém: Vi ABCD 1a hinh binh hanh nén trung diém cua AC cing chinh la trung diém cia BD. Nén lay toa dé diém A+C = Toa d6 B+D =D =(A+C)-B =(1;1;1)-(1;1,0) = (0;0;1). Cau 30. Huong dan giai: @ Tu luan: X47XuM = k(xR-Xu) Ghinhd ly thuyét: Diém M chia doan AB theo tis6 k khi MA=kMB @4y4-yy =k(ygp-Yy)> Za ly =k(Zg-Zy) kxg-X4 2xp-X4 Xy =— + Xy =——* = 2.-3)-1=-7 M k-1 ‘M al (3) e vy = aA, Ap dung vao bai ta duoc: yy = M824 = 2.4-2=6 kip -Za 22p - Za ty =o gy = 8 #4 =2.5-3=7 MO k=l Me 2-1 ¢ Tracnghiém: M chia doan AB theo ti sé 2 thi B 1a trung diém cia AM. Cau31. Hudéng dan gidi: ChonB Tu luan: — —. —. 4MB—. _ Tacé MA.MA =4MB.MB = MA= a . Khid6é MA;MB cing phwong. Ma MAMA = 4MB.MB =>(MAMA) =(4MB.MB) <= MA‘ =(2MB)' => MA=2MB. Do MA=2MB va MA;MB cting phuong nén MA=2MB. Goi M (x3 y3z).Tacé -l-x=2(3-x) x=7 MA=2MB & 4 2-y=2(-1l-y)@} y=-4M (7;-4)1). 3-z=2(2-z) zal ¢Tracnghiém: Cau 32. -Huéng dan gidi: Chon A @ Tu luan: Trang 561 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz xt u(t) = 28 1524+ 208 minu(t)=u{ 22) 4 3° —10r-+ 20 rr) gg menu(t)=u(-2)=48- vay d(B,A) dat gia trinhé nhat = ¢ 30, m{=.2.2). 11 11 11 11 A diqua A va u,=AM. Cau 189. Huéng dan giai: Chon A. ¢ Tu luan: Vay d(B,A) dat gia trilénnhat <f=-2> M (3;-4;-4). A diqua A(1,4;2) va u, = AM =F (286)=(1:-4-3). Cau 190. Huéng dan giai: Chon B x=-1+2t ¢ Tu luan:Tacéd Ary y=1-t =. CEA C(-14 2r1-62r). z=2t AC =(~2+ 24;-4—1;21), AB =(2;-2:6)=>| AC, AB |= (-24—21;12-81;12-21) = Vi8"? 261+ 216 = /18(¢—-1) +198. Do 46 Syage nhé nhat khi t=1 hay C(1;0;2). vay A qua C(10;2) vacé VICP u, =BC =(-2;-3;-4). Cau 191. Huéng dan giai: ChonD ¢@ Tu luan: Mat phang (P) c&t mat cau theo duwong tron cé chu vilén nhat nén (P) di qua tam I(1;-2;0). Ssane = 5 | AB.AC | Phuong trinh mat phang (P) song song Oxz cd dang Ay+B=0. (P) qua Inén suy ra phuong trinh : y+ 2=0 @Trac nghiém: +) P//Oxz nén loai D +) mat phang (P) qua I nén thay toa do I vao cac pt loai duoc B,C. Cau 192. Huéng dan giai: Chon A ¢ Tu luan: goi H,K Tan lwot la hinh chiéu vuong goc cua M lén mat phang (a) va truc Oy. Taco K(0;2;0). d(M,(a)) = MH < MK. Vay khoang cach tt: M dén (a) lon nhat khi (a) qua K va vuéng goc voi MK. Phuong trinh mat phang (a) :x+3z=0 Trang 591 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz ¢Tracnghiém: tinh truc tiép khoang cach tir M dén m6i mat phang, kiém tra duoc khoang cach tte M dén (a) :x+3z=0 1a lon nhat. Cau 193. Huéng dan giai: ChonB @ Tu luan: mat cau (S) cé tam I(1 ;2 ;3), R=3 Co IA < Rnén A nam bén trong (8). Tacé d(I,(P))=VR?-r Dién tich hinh tron nhé nhat © rnhé nhat © d(1,(P)) max =1A = (P) qua A , cé vtpt IA3(P):x+2y+z-2=0 ¢ Tracnghiém: Cau 194. Huéng dan giai: Chon A @ Tu luan: Goi H,K Ian Iwot 1a hinh chiéu cua C lén mp (P) va doan AB. Ta co CH = d(C ;(P)) = CK > d(C ;(P)) max khi H =K. Khi do (P) qua A,B va vuéng goc (ABC) >i, = [[4B,AC |, AB ] = (-9;-6;-3) > (P): 3x+2y+z-11=0 ¢ Trac nghiém: Kiém tra thay A,B thudc ca 4 mp néu trén. Tinh khoang cach tir C dén cdc mat phang chon duoc dap an A Cau 195. Huéng dan giai: Chon B @ Tu luan: Mat phang (P) c&t cdc tia Ox,Oy,Oz Tan luot tai A,B,C nén A(a,0,0) , B( 0,b,0) , C(0,0,c) voi a,b,c>0 3(P):2 + hse = 1 (P) qua M nén 142384153 © 3 abe> 162 abe abc 1 . 1 2_=3 Voane = ¢ abe 2 27 = Voanc min khi 7 = p=, Suyraa=3,b=6,c=9 Vay pt (P) : 6x+3y+2z-18=0 ¢ Trac nghiém: Kiém tra thay M thudc 3 mp 6 cdc dap an B,C,D. Cho cdc mat phang giao v6i Ox,Oy,Oz tim giao diém A,B,C roi tinh thé tich va so sanh. Cau 196. Trang 601 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Huéng dan giai: Chon A @ Tu luan: AB AC, AD . 3, AB.AC.AD =, AB'AC'.AD' 527 AB' AC' AD' AB'.AC'.AD' AB.AC.AD * Ca Vane _ AB'AC'AD' . 27 27 Taco 4= => =v, ay Vanep AB.AC.AD ~ 64° “°°? = Gq {Anco Vapcp nho nhat khi va chi khi ABT _ AC’ _ AD" 3 aR = aR =>B' (2: +2) AB AC AD 4 4 444 RIN Na? IN ale Luc dé mat phang (B’C’D’) song song voi mat phang (BCD) va di qua B' (24: = (B'C'D'): 16x +40y-44z+39=0 ¢ Trac nghiém: Kiém tra thay A,B thudc ca 4 mp néu trén. Tinh khoang cach tir C dén cdc mat phang chon duoc dap an A Cau 197. Huéng dan giai: Chon A @ Tu luan: Gia str (a) :ax+by+cz+d=0. Goi @=(A,(a)).Vi M,N thudc (a)nén a+b+c+d=0 d=-5b (oped 0° 1 c=-a+ 5 Ta duoc (a) : 2ax+2by+(b- 2a)z-3b=0 Cé si not] [4a 2b + 2a) a 4 fe + 12ab + 360 6 sing= = Ina |-Ju] Ve..[4a? + 4b? +(b— 20) ~ dab + 8b Néu a=0 thi sing= 8 ta tim diroc max f(t) = (3) = ~ 1? +12t+ 36 x . b Lebar eX Néu az0, dat t=—,teR. Xéthamso f(t)=—; a 5t* —4t+8 Do do gmax <2 (sing)maxeo? =2. Chon b=5,a=8. a Vay pt mp (a):16x+10y-11z-15=0 ¢ Tracnghiém: Kiém tra M,N thuéc mat phang (a) nén loai duoc dap an B,D. Tinh goc gitta dwong thang A va mat phang (a) dé loai dap an C. Cau 198. Huéng dan giai: Chonc Trang 611 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz x=l1 AB(0; 2;4) => pt tham sé cia ABIa: { y = 2 => M théa man phuong trinh: z=4t 1+(21) +(41)-4= 0-5 1-5 => M(1;1;2). Cau 207. Huéng dan giai: Chonc Giai: Ta c6 (1+ 1+1—4)(1+1+0-4) = 2>0 => A,Bcing phia so vai (P) Ta c6|MA— MB| < AB =>|MA— MB|I6n nhat khi M = ABO(P). x=l1 => AB(0;0;—1) => Pt tham sé cia AB la: | y=1 x=1-t => M théa man phuong trinh: 1+1+(1-t)-4=0<>1=-1=> M(11;2) Cau 208. Huong dan giai: Chon B Giai: Ta c6 (1+ 1+ 1-4)(0+ 1+5-4)=-2<0=> A, Bkhac phia so voi (P) Goi A’ la diém déi xtmg A qua (P), dla duong thang qua A vudng géc voi (P) tai H => pt x=l+t tham sé cia d: y=1+1=> Toa dd H théoa man: z=l+t (L4t)+(L+4)+(18)-4=0<> et oal $ 4, :$)= >A’ (2: win 5 3°3°3 3) Ta c6|MA'- MB| < A'B =>|MA'- MB|I6n nat khi M = A'BO(P) x=5t =>A' oe 2, 2). =(5,2;-10) => Pttham sé ctia A'B Ia: y=l+2t R337 3 x= 4-108 = M théa man phuong trinh: Sr +(1+ 2r)+(4-10r)-4=0 <=> t= ; =m(3 wim wi 2 3 CAu 209. Huéng dan giai: Chon A 2 —_ — —.2 —2 — —_ Giaii: Xet diém / thy §, taco MA? = MA’ =(MI-+TA) = Mi + 1A’ + 2MT-IA yo? pe ey? a? be MB? = MB =(MI+1B) =MI +1B + 2MLIB Suy ra MA? + 2MB? = Mir + TA’ +2MIIA+ 2(mi° + 1B + 21.) 2 yy? 2 a = MA? + 2MB? = 3M +TA + 2IB° +2MI(TA +21B) => MA? + 2MB? = 3MI? + IA? + 2B? + 2MI(IA+ 2B) Gia st JA+2/B=0© IA=-2IB, tacé toa dé cia / a: Trang 641 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz _X4t2x_, 142.0 1 1420 3B I yo dat2ye 2421 4 Hay (: 43) 1+2 3 3 3.33 ~ 2at2Zg 142.2 5 "1420 3 3 Vay, voi (: + 3), tacé IA+2/B=0 nén MA? +2MB? =3MI? + IA? +2IB. Do Icé dinh nén JA”, JB? khéng déi. Vay MA? +2MB? nhé nhaét & MI? nhé nhat © MI nhé nhat © M 1a hinh chiéu cia J trén (P). Duong thang (d) qua (: +; 3 va vudng géc voi (P) nhan vecto phdp tuyén n= (15151) ctia (P) lam vecto chi phuong nén c6 p/trinh (d):4 y=—+t - Toa dé giao diém H cia (d)A(P) 1a: a( ; Ola elz [5 NY - H lahinh chiéu cta J trén (P). e Vay M 1a hinh chiéu cia J trén (P) nén M=H Két luan: MA? +2MB? nho nhit khi m(oe M4 2) 99 9 Cau 210. Huéng dan giai: Chon A 2 —2 -. —=)2 —2 2 __— Gidi: Xét diém I tty y, tac6 MA? =MA =(MI+TA) = MI + TA’ + 2MILJIA 2 -2 > ry\2 2 2 o> MB? = MB =(MI+IB) =MI + IB +2MIIB Suy ra MA? + 2MB? = Mi + TA’ + 2MiTA+ 2(Mi° +1B + 2M.) > MA? +.2MB? =3Mi +IA’ + 21B° +2Mi(7A+27B) => MA? + 2MB? = 3MI? + IA? + 2B? + 2MI (A+ 2B) Gia st JA+2/B=0© IA=-2IB, tacé toa dé cia a: _X4t2x_, 142.0 1 “142 «3B I yo dat2ye 2421 4 gy (us) 1+2 3 3 3°3 pa cat Pip 1424 _ 4 1+2 3 Trang 651 Nhém Dé file word Nhoém Dé file word Chay én dé Oxyz Vay, voi (it), tac6 JA+2IB=0 nén MA? +2MB? = 3MI° + IA? +21B?. Do Icé dinh nén JA”, JB? khéng déi. Vay MA? +2MB? nhé nhaét & MI? nhé nhat © MI nhé nhat © M 1a hinh chiéu cia J trén (P). Duong thang (d) qua {ts +; 3} va vung géc voi (P) nhan vecto phap tuyén n =(1;1;1) cua (P) 1 x=—+t 3 5 . gk es 4 1am vecto chi phuong nén c6 p/trinh (d):4 y= yt z=34+t -Toa dé giao diém H cia (d)a(P) la: a(es 0.2). - H lahinh chiéu cta J trén (P). e Vay M 1a hinh chiéu cia J trén (P) nén M=H 1,10 3) Két luan: MA? +2MB? nhé mht khi uss > Cau 211. Huéng dan giai: Chon B Bang céch phan tich MA+3MB-+2MC = MI + IA+ 3(Mi +IB)+ 2(Mi +IC) = 6MI + IA+3IB+2IC Dén day chi viéc tim toa dé diém I sao cho IA+3/B+2IC =0 => |MA +3MB+ 2Mc| = mil Chi ¥: JA+3/B+2IC =0@ O1 =2(04 +308 +206) of = =—(x,+3x,+2x,)= Suy ra toa d6 cia I 1a 4 y,=—(y,+3y,t2ye)= wit aIN alr © _ als welts (z4 +32 + 2%. )== a aL ole ale =>M 1a hinh chiéu cia I trén(P). Goi d 1a dung qua I vuéng géc voi (P) => pt tham sé cia d la: j y=—+4 nN i | + ~ Khi d6 toa d6 M théa man: [Z+1}+(Z+r)-(Ze1}-4-0=3 > (3 Cau 212. Huéng dan giai: ChonD Trang 661 Nhém Dé file word Nie WT us Ne