Tài liệu hình không gian 11, Essays (high school) of Mathematics

Download Tài liệu hình không gian 11 and more Essays (high school) Mathematics in PDF only on Docsity! NG9C HUYEN LB OANDA St¢y & e+ Psy yo HE THONG DAO TAO PHAC DO TOAN C6 Nooc Huyén LB BON (viét tat: the Best Or Nothing). C6 mong cac trd lun khac cot ghi tam khi chat BONer: "Néu toi quyét lam gi, toi sé lam 16 mot cach that ngoan muc, hoac t6i sé khong lam gi ca”. Tai ligu hinh hgec khéng gian 11 Ngayhoc__/__/ TAI LIEU HINH HOC KHONG GIAN LOP TI +++ DANG 1. GOC CUA DUGNG THANG VGI DUONG THANG Dé tinh géc gitra hai dong thang d,,d, trong khéng gian ta cé thé thu hién theo hai cach Cach 1: Tim géc gitta hai dudng thang d,,d, bang cdch chon mét diém O thich hop (O thudng nam trén mét trong hai durdng thang). Tir O dung cdc durong thang d/,d, Tan hot song song (cé thé trong néu O nam trén mét trong hai dung thang) vdi d, va d,. Géc gitta hai dudng thang d,’,d,’ chinh 1a géc gitta hai dudng thang d,,d, . Luu y 1: Dé tinh goc nay ta thudng str dung dinh li césin trong tam giac Bic -a 2be Cach 2: Tim hai vecto chi phuong U/l, cia hai dung thang d,,d, . cosA = Khi dé géc gitta hai duwdng thang d,,d, xc dinh béi cos(d,,d, )= | . Ala 1 Luu y 2: Dé tinh uu, iu, | ta chon ba vecto a,b,c khong dong phang ma cé thé tinh dirgc dé dai va géc gitta chuing,sau d6 biéu thi cdc vec to u,,u, qua cac vecto a,b,c ¥0i thurc hién cc tinh todn. DANG 2. G6c GIUA DUONG THANG VG6I MAT PHANG Goéc gitta duong thang d va mat phang (P) 1a géc gitta d va hinh chiéu cua no trén mat phang (P ). Goi @ 1a géc gitta d va mat phang (P) thi 0°<a<90°. Dau tién tim giao diém cua d va (P) goi la diém A. Trén d chon diém B khac A, dung BH vuéng géc voi (P) tai H. Suy ra AH 1a hinh shsCouing g6c cla d trén mat phang (P). Ve Ib page "Hoc Toan cé Ngoc Huyén LB" dé dang ki hoc ql NGOC HUYEN IB QANDA Sty Tai ligu hinh hc khéng gian 11 & e+ Per oe wo Vay goc gittad va (P) lagoc BAH. Néu khi xdc dinh géc gitta d va (P) khé qua (khéng chon dugc diém B dé dung BH vu6ng géc voi (P) ), thi ta str dung céng thirc sau day. Goi « 1a géc gittad va a(M.(P)) AM Ta phai chon diém M trén d, ma cé thé tinh khoang cach duoc dén mat phang (P). (P) suy ra: sina.= Con A 1a giao diém cia d va mat phang (P). Dé tim géc gitta hai mat phang, dau tién tim X 5 5 giao tuyén ctia hai mat phang. a \ Sau dé tim hai duong thang Tan hot thudc hai mat phang cing vudng géc vi giao tuyén tai mét diém. Goéc gitta hai mat phang 1a géc gitta hai duong thang vita tim. Nhiing trudng hop dac biét dé hay ra: - Truong hop 1: Hai tam gidc can ACD va BCD cé chung canh day CD. Goi H trung diém ctia CD, thi géc gitta hai mat phang (ACD) va (BCD) 1a géc AHB . - Trwéng hop 2: Hai tam gidc ACD va BCD bang nhau cé chung canh CD. Dung AH. LCD>BH LCD. Vay goc gitta hai mat phang (ACD) va (BCD) lagéc AHB. - Trwong hop 3: Khi xac dinh géc gitta hai mat phang qua 5 tanén six chung cdne thitesau sing = (42) khé, ta nén str dung céng thitc sau: sing = —_——~ . d(A,a) V6i ~ 1a goc gitta hai mat phang (P va mat phang (Q). A lamét diém thuéc mat phang (P) vaala giao tuyén cua hai mat phang (P) va (Q). - Trwong hop 4: Co thé tim géc gitta hai mat phang bang céng thitc S’ = S.cos 9. - Trwong hop 5: Tim hai dung thang d va d’ lan luot vudng géc voi mat phang (P) va mat phang (Q). Goc gitta hai mat phang 1a géc gitta d va d’. - Trwong hop 6: Cach xac dinh goc giita mat phang bén va mat phang day Bude 1: Xac dinh giao tuyén d cia mat bén va mat day. Buc 2: Tir hinh chiéu vuéng géc cua dinh, dirng AH Ld. Bude 3: Géc can tim 1a géc SHA . fer dinh, A 1a hinh chiéu vuéng géc ctia dinh trén mat day. — |/<____— th page "Hoc Toan c6 Ngoc Huyén LB" aé ang ki hoc Gill