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i M * 3D Gaomele ny . Stwagght Lana! 1, Gqcorkton of a, Straig het Aine, pas vim povert vy paraltet Ahrowply @ an iv vector: > to a q 2) 4 Se - bs @ Voclor form } w= A+tb a Pp 4 [e = porameter| e Cartesian jlorm: b A= CMs 7) R-X -y Z-4 — +=. —=t p= A Abs mj nk p= aityy 2h: e Gn - favametye Vector qu” + (#-a@)x = 8; om” Cyvocttow ob a Heal gfct lune pee ther vo given porate > ugh A fe Fae © Vactor jor: e = O+t (b-4) Pee © Cortestan form: L-% yey 2-2’ A= (197i) ak Pes eae rT B® CanJar¥). = 5 ° Non- pavamerlee Nactor Guu": > (@- @) x (b-8) = ¥ Angle PMetwoen Two lonest wT > > 40 .-,e @4atd 0 Veclor fowm : m= at > Bb: eal. B = Cos in Ib] [2 oyoshish Saha e Comlestan joran ¢ Hey I-Y F- 4 We % aw zZ-% , = 1, BH . 5 ; = aA bj | 1 ‘ 2 AA, bi boy Fore | -t @ = co N a4 4 a? A a,?-+ b+ a* ¥ Qkow. Lines! “Two Wnog whieh are hetther wrlersec Hn nor dpa wrothet ave called Skow Itnas, d ® Shortest distance between Iwo Aine? 1. Showtest déstance betwean +wo MAeccactay Agnes FS Fev, _ 2. Paralick Linc? P= 0, +4b = —_ foe eC= ++b =: = A = |b x (a,- a) | |B F =) ae 3. Skow lames! wa at &b, hy R= y+ 4/5 ae ad = —~ Mie, (a, - a )- (b,x B) | = _> ) b,% b, | ; LX Y-s zZ-2z @ Cariesianw TMme Jt e Lo = ! arlesian 4° l a, by ro R-% _ Y-Y2 eo > = = . Aa ay by So so a oT ee a 4 by Cy A= ae be Co 2 { (- br)" +(q a,- %%) +t Cab, ~ 42s) Coyoshivh Saha 2 Equation of. the. pane whon ctbs-lance [eon the il and —untt norma *¢ grmats _—> r © Vocclor how Y.A = Pp. fh — Unicel normal pr distance | © Carlesiaw fora: A s 4 rm nm= At -+ my + Zh Aw+ hy +NZ = P: 3, Equl™ of the plane pacing throug @ ‘le port MR porated to wo vectsre? ° = © Veet form - p= + then? L a Aivan pont parallet +o b he] ° Cavtestaw Lorem: R ~ ~ ) a= ate y jg +a Mn my Dy da) 2-2; sis F. ~ 7 ¢ in i a. b= Aitmy + hy’ ‘ = Q e a 2 4, ma ho = A,t tmnythe eNSn pora martrte erm: [Cr- 8) es z] alg glee] =Ceee). 4 Fquattow OL the plane passing Uru lyon gies porns QR poweties, to ay : a veetor? @ Vector am * + Z.b — potter = — = a,b fe nw = a+ s(b-a) + tts Veeteos af point, portlet to wv). e Non - poranust ric : Lew 8) (b-%@) ca =0, Coyoshish Saka 3D Geo ma-| VA ' 3 . iz i ® Cowlestaw jer: ne ax, aly, | 42, mE yoy a 2 ra eeu Tt we ' b= Xt t4,J5* 42 Ay % y-Y Z,-%,) = 0, a zx ae net Bix Lia my + OK, a wy wy 5. Equarttow oh, the plans passing. thro up hwo given non— corlineay poids + © Vectow form: as = a+ 3 (b- a) + t(e-a@ [ O,b,e — pasion Mectsrs of pant : e Non-parametric + [(#-a) (b-%) Ce-0)] =o. © Cavlesaw ferm! RR Yr dy Z- 7, Ve~ % Se -Yy Z,-71 = 0, 3 2y J3- 41 y- Fi 6; Cquattow of a lane Passing dhrrotp hy the Aine at qrtersactiow a- Awo ‘al plies * © Vector form qs af. plane passing “Theoupe the airs oF crylaxsocitow of plones ery = q, & FAG, os (@R- Ht > CF 4) =? O;et by +c z+a, =0 e Carlesiaw fern < ky a,x + by +O, 2+ Fe O. =O. + a, (ayx+ biy+ Cet a) +d (a% baytca?* ? Goychch Sek Coblonar ty of -two Lames . the aqu" =f. 0. plans 4 do=o, Abo 9 XY,% Gres iwlorcapt wtf = = pay Conch ow (a,~@, ). c b, Xx b, ) = 0, F i, eee Yas 7,77) a, b, Cy =0, a, b) my * Ang ke between —wo planes > Mong = Vy 4 Angie between & i) — = pS a+t+tb _ v = = h Wn, = Vy p= cost | BPs | ny ny Jaye. aa a pranc! pa aod » gor | 2 br ; A Equadtton of. b¢soctors of the angle hetw.e3ew -+wo planes: Ox+ by + ez#+aA=0 [ dd, dol. Qn + by +0 74+A,=0, ax +by 4czt a 0,% + by 4+O,2 4+ Not+b*+ 2 aa, + bb, +c, 50 
