I' 'tiww &,oeL ?"*tt"5 - 0n rAp Hir.Ju Hoc clAt rics TRoNG xs0xc GIAN t I vtrr PHLPgNG D4ng 1r Ccr rniNn ruAr PHit'tc bin B[-1;1;3J va mat oh'Ang [P): 83 Trong kh6ng gian vsl h6 toa Orvz , cho hal di€jm AQ;a \'vu6ng g6c vcri m5t phang [P] D/s: vi - -?,,-)- -5:0.Vl6t phuong trinh mEt phing [Q) di qua hai di6m A, B ,Qt,2A-3;-11:0 phuong trinh mit phang [P] di qua har didm '{r 2: 1: ' B(1: -2:1 HT 84 Trong kh6ng gian voi h6 tga oo Oryz , vidt HT \ J, t a4 T vi song song voi duong thing a v : - _i _ -')r D z Dls:(Pl ii.c- j1, 'r- -9:Lr' HT 85 Trong kh6ng gian v6i :-) i,,-l -, : , , r'l t-'' :t: HT h0 d'' + D+ tQa d6 Oryz, :! -,\ := '-1 693 cho du&ng thing (4) vir (d.1c6 phuong trinh: Lip phuong trinh mit phing IPJ chria [d,) vi (dr) ' D/s:{P): Y+Y-52+10=0 mat ciu tS) c6 Phuong trinh: Orqz , cho dd 86 Trong kh6ng gian voi hC tqa vec rry : : , tl:: ,' - !t't + z2 *2t+6y 12- 2:A Viert phrrong tr)nh m5t nhang (P) song song vor gia cua ru6nggocvmmitphang 'r i - l, -: - II L vAtiepxircvdi (S Dls:(P):2.r -y -r2z:3:l: hoac (P): 2r - l-22 -21: tl' ' HT g7 Trong khong gian v6i I :+ ,,., -1r:J phang :1.j hO tca de 0:;: cho drem lvi[1; -i; 1., r: -al diron3 thing ir],; ; '= t -t - -, p\u:ng r-r-lir Chfrngminh ringdidm i1 d.,.,?, cirng ndm tr0n md?m5.npn5ng 1r;!" d6 D/s: t: r2Y -.2 r ? : '- lr-rit- ' Dang 2: Phucrng trinh mit phi'ng li0n quan t6i mit chu HT 88 Trong khdng gian vcYi h0 toa :) - !-l) - ;l - ?x - 2,' *'\z * : xirc vdi mit clu [S1 (P), :t 22- 3-2Vi:t; Dls: dO Oru: LAp phr-rong , cho dr-rong t'hing :r, "!_3 va nrat ciLi d: t;: T - - trinh mat ph;ng (PJ song song v&i d vi hodc (P), trLLC [S1: 0x, dbng thcn tieP y-22-3- 2r,5:0' vAmitphing[P] Trongkhdnggianvo,rh0toa dO Oru:,chomitciu[SJ: rr -!2-t2-2''-1';-]:0 mitphing [PJ vatrep x'ic + j -3:0.vidtphuongtrinh mitphing [Q) dr quadidrn '1,Ii3:i: -1) vuonggocvoi vryi mat ciu [Si : D/s: (Q): 2t + -2:-9 : O Hoqc (Q): l:t *7a lz-9 HT89 Cdu hoi yri tvqno tLr: (Sf , 12 = y2 + :2' -2r - L'J DS: - iz i5 : 0' 1P' : 2r - I -6'-5 : (Q'; 2r'r29 - z-6:a hoqc (O) C''11(l:1;2)' I11r-iOy 22-5:a' Trongkh6nggianv6i hCtoa dd Orlqz,chomitcau[S]: 12 =92 -'2-2'*1'l*22 c6 bin kinh r : irinh mit phdng toi.no, truc ox r,) cit mit c;u [S] theo m6t dudng trdn Dl* Q):Y - 2z = HT90 HT91 Trongkhonggianv6ih6toa dd oiy:,cb.omitclu[S]: 12 -!'2 6>v arrrrrrflrr an\r cE I.t -3:0 Vi6tphugng ' -:2 +2r-2y-22*7:0 viduongthing EFN Pase 27 -;lr 'ffiTil.fr ur ' \ BJ s* - l{* HT113 vA it r - 6: u \1* :t-e Trongkh6nggianroa O:tu:: chocacdi€:n l(ll / r *211 lP;: TRiNH DI.IONG THANG : thing , d :',) L,_1 j ? _3 115 Ti'ong kh6ng gian viri h6 toa d6 Oxyz, cho dudng thing [d) c6 phlrnng lr:hl: { - - i : tr : -1 -'2t : - l -:- t [t = ,q] vi m5t p]ring [PJ: 2.r - u -2: -:] - il Vi6t phLrong trinh tham sd cua d,;ong thing A narn trOn , vi [P], cat D/s: vu6ng g6c v&i (dJ l.i J : I j,r7 I l:: rIT PHLTCYNG trinh clucrng thing bing c6ch xic tlinh vects chi phuong ,.-') t ,, mai phang P 114 Trong kh6ng gian vdi h€ toa dO Oxyz cho cluong thang ,l ' ; : -11.1 ,i l) : - i : t) Vrdt phuong trinh duong thang -\ di qua -111: 1: -2 , song song voi mat phing {P; v) vudng gdc vdr drrlng HT j VIET HT !- ir;.Bir:2: i) Vi6tphuongtrinhmltpheng[P]quaA,B ll: cho tam gi;ic ABC c6 di6n lich bans - )z- : Dang 1: Vi6t phuong l": * !, ). cit truc 0z tar M/sao DS: tS) &fu" ,t *taivz w 116 -;J t - ' Tror-rg kh6ng gian vcri h6 toa d,6 Oxltz, cho di0m phuirng tr)nh cfra dud'ng thlng d di qua tli6m 1"1, cit vi M[2; 1; 0] r,i ducrng thang Lip vuOng goc vai a Ox1,2,61'r" mitphing iPl: x + 2y-Zz + I = vahai diem.ii(1;7; -lJ (Dl phuong tliang Ia hinh chidu vu6ng goc cua duong thing AB trOn [P) trinh ducrng 8(4;2;0) LAp Gqi (U la mdt phdng qua A, B va vulng goc v1i (P) = (U, Bx + 7x + i1'z - 46 = HT117 Trongkh6nggianvoihEtructoadij iD) HT ', = (P) 118 Q) suy phLrcrng trinh {D) Trong kh6ng gian vdi hC toa d6 Oxyz, vidt phrrong trinh hinh chi6u vu6ng g6c cua dLrong thing n- t\ " l,'{ '''- ] -'i-t t'' [" : |t.t.:++tllt1 t Ef s:1: trdnmltphing P.r.ail ': r-5-0 r1r, lr:!-t,lr ,, l" l : i- tot t Cdu hoi tvong tLr a) V1i d r -1_ r-1 [': r : 1!t 29rrt I t^ I" HT -.)'1,r, ) - Jltt, 119 Trong kh6ng gran voi he tga dO O.x,-tz, ggi A, B, C lin }trot giao didm c0a mat phing P : 6r -2,t= il: -6:0 r,6i 0x 01t,Oz LApphuungtrinhdulngthangddi quatAmduongtronngoaltieptam grAc ABC dbng thoi vu6ng g6c vdi mit phing (Pl Hoc v0 Bg - cHUyEN cAtt sE oEN sEI{ Page 31 Ir:i -: Cl l:t J : :r D/s: d: ].,, t') - Zt I L / -r I - I - rlr 120 Trong kh6ng gian vdi h6 toa d6 ?xyz, '-) , r-l u-l -',_ 2 IIT phing vdi dudng thing IABCJ vir vuong g6c ' ') L2 ; -l cho dudng thing d -1 -I1 trinh dudng thing Ii6n quan il6n m6t Dang 2: Vi6t phuong didm A(L:2:-\).8(2:l:1;:C(():1:2i v) thing khic Clucrng HT121 Trong kh6ng gian v6i hC toa d6 Oxyz, cho didm M[2; 1; 0J vi du]ng thing d c6 phuong trinh ,i , "' - : {+ : :- Vi6t phuong trinh cua duong ihing di qua drdm IvI, cit va vu6ng g6c vdi duong thdng d lr vi tirrr toa d6 drdm M' d6i xirng voi M qua d :t | ' -l -l '-j= D/s:J ' t Cdu hiti tvongt?': a) iv[i-4.-2r-1 H'l'1,22 l/'lll,l -: -1, ;i ;j' -;i ):11 ,- ,, ) - - - ') clLl'rrng ') thlng d l -: - !-) i-r'ong xhong gian v6'i h6 toa cl6 Oxyz, cho dLrong 2z r - l-Ap phiro'ng tnnh z-i) \ DS: _1 - : ;t22 rhang,l song song vdi nr5t phing [P) dr qua ) v) m5t phlng [P]:.{ + 3/ * ,[1(2; 2, 4) v;; cIt drrcrng tirana Ia) I l)-il egiirjitu'sn.a i; : - L- ') b)d ; tLt ' - I.)L HT 123 :'-.17 t ): -'2 - !, lr' :.1 , r-1_ iP):2r-ry- z -r-1:0, I'I(1:2:-1) ,.Si A 2*9-5lt-2 ,) 3.: - : 0,,11(3;-2:-1; Trong kh6ng gian voi hd toa d.6 7xyz, cho Br2.9.li) Goi t.f-iAh)nhchieucr-ia,{ nin'r mrit'ph5ng rT v-i1 -'t I ', ':) :::_ -) j' i (o) dbng tho'i I DS: mit phing z*l ,'_) \ -6 (cr) :l.r -2u - : -21) - va hai dr6m ir 1: l:tj) vi B tr6n (rr) Tin}rd6dAidoan l:F.Timphr-rongtrinhduongthing J cua \D vcti to r,') J vLrdng g6c vdr ,{8 di qrra giao didm ;t t r+ HT 124 ,Pr:.i: Trong khOng gian vcri - 2tt hO toa dd Oxyz, cno m5t phing (Pl, :II:! -z:0 {?, i: -3ri-32 1:0 (dt :+: tal v) duong thang [d] t, ' IAn luot c6 phircrng ti'inhr tarpphLrongtrinhduongth5ng-\nimtrot.rg [P] song song vdi m5t phing (Ql v) cit duong thang [C] BE HOC VO BCT - CHUYEN CAN SE DEN BEN Page 32 tt -2-') HT I 125 Trong khOng gran v0i hOtoad6Oxyz,cho3di6m'-lil:2:-l)'13i'21'l;'CrU:l');v)dwongth-ng *"t :-:-: - ') : LAp phuong trinh ducrng thing 2 -i =, pheng [ABC] v] r'uong g6c voi duong thang [dl r-2 lt-I :-.1 D /s: -t t2 -11 11 A dr qua truc tam cua tam grac ABC' nam n'lit rnit phing iuong:hang I :: HT 126 Trong khong gian vcri h6 toa dc oxyz cho dtam ii.),: -1.1 -:: !p) r tt :z-it:0.Vidtphu'crngtrinhcuaduongthangd d1 quadremA namtrong(Plu;iop'diducrngthang f m6t g6c Dls: 1:rir Hoac d d: , t-:l HT u-2 727 Trong kh6ng gian toa db O:*yz, cho dlrons thang d: ) \ri6r phutrng trinh dirnng thing -\ :!: *,t *;: ='2: t) Goi iv1 li giao di6rn cua d vi IPl | r vudng g6c vcri d d6ng thoi khoAng c6ch tir M t6'i l - a! nanr r:()ng mlt Phang (PJ, bing jT l' I : -:) :1 HT12B,.frongkhonggrarlv&ihetoac10o,t1,zchotnitphangirJ:,.,: I , [rt] , t'' ' ': l1 r'i i-r) ch6o nilar-r u.ra khoing cAch gt'"ra thl"'g l'o''g t _ l'-'' hodc rl ,lri: -i [::-, trinh dtro 3rVirit HT 129 thing Ii6n uan thi kh6c g6c chung cua hai duong thang Trong kir6ng gian vor h0 toa dd Oxyz, vidt phuong trinh {wcrng vu6ng Ir:3=ii I \, al6n hai ducrng I -1 ,: \ l, L, vd J.) - -l ,/ l::1-:rt D/st HT130 Trongkhonggianvoi h0toa ddAxyz,vidtphuongtrinhduongthingddiquadidm 'iIi l: -5: [ r ,.1 =tr_n r_!_tr_i - ::v) tr,t : ; : ; r, haidrrcrng thing: ,1, 1;'- ,;'= [" tI i - -= 'nr, : -5 l:I -;J-i = 'll vicltca :_L = I D/s: ' d: 1l )- 2t i nffnl pflnt Pase 33 -i,E f " - I 't._: -i-i -1- ,r, ]; D5 2t l- [.r'=3-21 b)M(3;la, HT131 1),Li +:+ DS: Trongkh6nggianv&i h6toad6 Oxyz.,cho hai dudngthing i, _ )_, r-r '-r r-r* t-t-+ 112 l'-i.,-,-;-,J; \ I-2: i l: f, +,,.,#:3:= giao didm cua -\, vor I a I d6ng thrri cat ti.) D/s: r l I,- LI , r!:]:_],,:,r' l:=; zt A Arr.'im5t phingInJc6phuongtrinhli n;:.7-,; +;-'2:tt Vi6'tphLrongtrinhdLrongthSngddi qtta r'a vu6Irg gric v&i truc Oy, rr ii,t r:1 Trong khdng glan vor h01oE iolx-;'z cio iiu'r:ng th;ing 11, I : ,- 2/, clLrong thang t1 l) giao tuy6n.u, l; - i-2i hat :rat phSng [P]: 2r' ti - t t'a [Q]: l: _ r.'- l: 1,- ''t Go? li giao clidnr cita d, rl' Vidt phrrcrng trinh r dLrcrng thing d, qua diem A{2 3; 1J, dong Lllt cin dinh HT thryi r,7, rl, IAn lucr3 taflB va C c}to tam glac D/s:ri {r :2: lt -='.i.:::1.-'2i L 'I'rong kirong gian vni he toa ci6 Oxyz, 133 cit hai dr-rong thing 611o nrat ph)ng [): 1.: :] - i l: - ll va hal ciucrng thing d1: - = l-,ll - 1, 1,-1 = - = a:r.Chu'ngnrinhring:l ,,'aJ:cheo.:m;ii 'r'ierphu'o'ngtr)nhdirirngth5rglnarl :1.1.12 trin IPJ dring rhot \ c-it c:r ri: va dz D/s:-l - = ;) i -l HT 134 Trong kh6ng gian vcri hO toa d6 Oxyz, cho hai mit phing v) har dudng thing c6 phucrng trinh [P): l =r-t: ] (d.) -:J-':-j=t-: 1\-:l -.1.? , ,t y2[Q1: ir-J,-ttz-,:,.[dr]: !1 i':;i1 Viet phirong trinh drrong thang [-\] song song v&i hai mat phing (Pl, ta) vi cat (drJ, [dzJ ii - {' l::,-1t,,-26: D/s: [,\) -l- _:j _ lr :, i+r i HT 135 Trong kh6ng gian voi hO toa d6 Ox1,2, 96 mAt ohing [P]: 2:r: ' lj :22 - : vi hai dwong rhirng (d:), (d:) VIC'Iphrrongtr)nhcluongthlng(\l lAnlrrotcophuong1rin1',' }: +-t " -:=-va+'l,l : : : -1 song songvoi mit pheng [PJ, cdt (ir,) vA (d") taiAvi B cho AB = ._.) ,-1 -l 122 HT 136 ' I I L Trong kh6ng gian v61 h6 toa dd Oxyz, cho rr-L r , " g6c ? ,,t r : J-j -'= j "': vdi a vi cit ,C, tai didm ,,-: 'i-1-s -':, z E c6 bD rrn _) - mit phing [PJ: 2x -.y =; = 1: vi hai du]ng thang " vi€itphtrongirinhdLrongthSng-\so)lgsongvoi [P).r.'rrdng -'llcLPrru ho)nh d6 bdng rr^ Dry arrrra/crr r a rr cE n#rr odrr Dtoo 2A- | ,, Dls:A - 1: T t -a :6-t r+S :,,j -6 : Trong kh6ng gian vdi hC toa d6 1xyz, cho hai duong thing HT 137 ,t:t y- 2- t '2 Vi6t phuong tr)nh duong theng (dl song song v6i truc Ox va cat (dt) tar A, Cal [Cz) tai B, Tinh , l * t/ - t D/s HT -i;2 l''- -16 d Y: lJ - 138 \.11p1 :12 Trong kh6ng gian vcli h0 toa pl1yn.;1q trtlh ir l,I Ir l" l,='ii, HT 139"l'rong D/s A: dlr i,-ng tirar-,g c16 lhing: [d1l: Oxyz, chtt har ducrng idl s9n31:i:lrg ;ir; r.l - *i -_il) - li 2.1 va y*! {-d2j: ) ') :t kh0ng gtan rzcrt h6 toa cio l')'i1'7' cho cic diem Af2'{J'ii); B[0'a'0J; cl-2'4'6; \ tt Viet pirrrcrng tt'rnh dtrdng thang A / / ! -l1-" , Iri: -',tu - -]- -r, j ld) vA cat cAc drrong thing AB, r'a d,-rnng thane ldl: OC lJ, j'; ',-(' ) Trong kh6ng gian vcri h0 truc roa 116 Lr.xl,z, cho b0'n didrn A[.1;5;61; B[0r0;1); C[0;2;0J; D[3;0;0J ChLrng minh goc vcri nrrr p]rang O'x-v va cAt cic cAc dLrdng th;ing AB v) CD ch6o nhaLr Vidt phirong trinh dti'irng tllSng fci 140 "'r-tirng du'ong thAng AB, C) HT "rr/ - r.ii il:l r.'.) ,:ii ca i';ll dti'rvrirl tlSng i.i7'r, r-, l:=" J Irr'" l''t-:lt HT : 141 Trong kh6ng gtan vtri n0 toa d0 O,tyz, cho h:ri tlr'rtrng thing c6 phucrng trinh: lr : -r - zr ,1 ri;:: vi ]' ,-, I d, cit trungvdi gdctoad6O, _.Xetu,t+i,tuongd6i ciadrvad:,ViStphuongtrinhduongthAngdquaivl I:;- dr va vu6ng g6c vdi d: I,.:' I D/s't lr: -, l': I CAu ) hdi twdng tV; 1,, a) VOr )i;1.7.L; , I *I _ ZL I i!l.j -i:tt 2+t ES; ,l :r'-1 : 31 L1-l l 1.,: t I va [d:]:1!:l-t Trongkhong gian voi h0 toa Oxyz, cno dLiong thing c6 phucrng rrinh: HT 742 (drJ I lz:0-2t L_, - l, jir:31'-i,.Goi KI) t'- l': -i;11 hinh chi6u vu6ng g6c cua di6'rn tr6n {dzJ Tim phucrng trinh tham s6 cua du}ng r thiing di qua vu6ng goc vdr (d1l K lx vi cit (drl I 11\ 11 (ri 12 ) " l Lt ,], \ -,)\J/\ -1-t.l 11 HT 143 Trong kh6ng gian voi h0 toa d0 0;;lz chc drdm [0;1;1] va ducrng thang [dii [d;] voi; (cirl: 't - i: li -') :i ; ]i giao tuven ciia I r.et'-rl-,anr t.P., - i : rl ,.,a IQJ : :' , ,; : ) - li \/i6t phLrcrng iv1 ) I i [c]rJ trinh du'ong thing [dl qua D/sAM: i M vLi6ng 96c rd-] [d )'"a ie: 'i't-L=,=] ): HT 744 Trong kh6ng gian ;cvi h0 ioa ii .i i U- l ;i | P-1 I : ] -) D/s r : ' - 'l vLrong goc \'(ir duong HT145 t- C.:.,r ) ^+,.r^-.1,,,;.,.-rLinor\,.i^.irnn.rr,rirrhi *rhing r,i1 va cat JLr org l: : 1; \r) dt|crng tirars z, :ho :rat pirang r^ I :ra:e :', - Trong khOng gian vcri h0 toa dd Oxyz, cho n-.al pha;rg rP]: lx - -' , 1::11 iPl, vu6ng g6c vdi drrd'ng thang [dr) vA cat dLr ]ng th;.ing i.i-'1 irr d,enr E ': ' r:nn , : ir C0 bang 12 h-r ':'Lr '.'nr :hang [d:]: fr-ll-t I Dlsr!:].-; l.'-tr t HT 146 Trong kir6ng gian vdi hO toa Oxyz, clto hai didm A[0, 0;-3], B[2, 0;-1) vi mat pheng [P) co phrro'ng tr)nh: q-' 81,, :7; * 1:0 ViSt phuo'ngtrinh cninh tic d.rlng thing d nam trOn n-,at phang (P] r'i d vtiong goc vtri AB tar giao drem cua drrong thing AB vo'i IP) , -) : ' HT't+7 'I ,, -! -1 l Trong khong gian vdi h€ toa d.o oxyz,cho har cluong thing" - 1: ,12 y - :' - ua mit phing [pl: r - !/ - 2: -;] : t) , dr j L : +:::f ) -L ; t dr: vi6t phuong trinh duong thang -\ nin.r tr0n mit phang IPJ vA cit hai duong thdng d1 , d: , t-' D/s:A:' -':I: i -i HT 148 Trong kh6ng gian vdt h0 toa dO Oxyz, viet phLrong trinh duong th5ng [d] g5c r,6i mit phing 1/ i-,,-:- i r:::D/s I l-ndbngrhcyi catcahai du'ongthang ,; ) == ":- - I: va -I i -l ,VC/I irll I od.r rrA piv rrrrrtrilr rhr.r ci niu pf,u PasP 16 (Pl .1 Lt, I tvang tV: Cdu h6i a) ltni (P): -lx - J - iz - : A, :L:*l trt P t -7 ') " " ') z*2 215 b) Vai 'l'1:2.t: t1 i: - : tl , d, f-t y-l i DS, HT 149 , :r-2 tI'r-2 ''r,i1.:,1 I !l-2 Trcng kh6ng gian v&i hCAoE dcfDxt,z, cho ba mat pheng: [PJ: z -11 2r !; i -,: , [QJ: Lr !' q - 2.: - l]: lr, '1:*i-tlvaJu'ongthingA, i_:l:!:]:: Cqi 1,, ligiaotuye,cua(plvatQl.VietpSuong ll:.i r.i-rr'li lirrrrttll thin;1 [r1] viri,:tg gr-rc',,ri ilil ,;:.r ,:il ii nai iirrirttq t)ring -.:, -i, [R] : D/s HT r-'),:1 i ,_ d: 2;l - r 'l I 150 Trong khOng sian vfvi h6CIto8 d6E Ox-r'e, ciro ba drrdng thingc6 phrrcrng ''2 ,l ,lt L ,.,i D/s: ti., ,1 ' '':t i, " r"-'-"D -'-"'' I lAnluottai cacdidmA,B,Csaocho,;1 R - U(' \ Dang 4: Vi6t phucrng trinh duong thing lien quan d6n khoing cdch ir -IHT 151 'l'rong 1ti rrnr rrA niy n:rrrrrfirr cho AR n'i.' : cF : : vidr ,,jt - _: : : v) didm 11 i: t:ri,, trinh cia mit ciu Duong I ISJ I D/s: fSJ: -U-\2 -(z- (:i!:ts {.c*7)2 Trong kh6ng gian v6i hC toA d6 Oxyz, cho mAt phdng (d 2r * y - 2: - ,l : vi mat c'Au (S'),.r2 o !t) + ,2 -'2., [!i 8; - L] Xet vl tri tr-rcrng d6i cira mit chu [S) v) mat pheng '.,.) Vi6t phuong - - - HT 167 trinh mat chu [S'J ddi xung vsi m5t ciu [S) qua mAt phing i1i ' E/s: (S'l : i:r - 3.i HT HT - g) -:- ::.1 :2it 168 Trong kh6ng gian rr6i hA toa Oxyz,)Ap phuong trinh mat chu [S] biSt ring mit [P]: : : lhn luot cit ISJ theo hai dr.rong tron cd bdn kinh blng vi B D/* (S): it: - o1! -:y - tt,2 -,r - 1U,1 : 261) (a, b e R) phing Oxy vi mit phang 169 Trong khdng gian vdi hO toa Oxyz, cYLo mit phing [P]: 2.,: - rt - 2: I - U v) duong thang d: I 'u'ri t-l.Vietphrrcrngtnnhmatcau [S) cirtAm lt].rr-r6cd, IcAch [P] m6tkhodngbing2vA [P] cit[SJ *) - theo nrdt dr.rong tron [CJ crj bAn kfnh bing a' H't 170 Tror:g khdng gian vri'i h6 toa dd Oxyz, ch) Z dieim,\i0; tl; al, Bf 2; 0; 0l LAp pirLrgng tr)nh nrat cAir ISJ di qLra O, r\, B r.a co l[...]...' vIfT pHrroNG TRiNH rvrAr cAu HT161 Trongkh6nggianvdi h0toad6 Oxyz,chodr6m lL; -2: ) Oy E/s: (:r: _ i,2 -iy *212 - (: - 3 j2 : l0 HT 162 r ri, : Trong kh6ng gian vdi f,:zt [r: : t vA d, : : : [ l.: vu6ng g6c chung D /s: (t: Cdtt hot 2'i' - - r/r d, trinh mit cAu ISJ c6 duong ch6o nhau ViSt phuong... ltj - l.r - 1,: : I [e=0 Trongkhdnggian r,&i ij, i cri phuongtrinh {.2, :2i ,1/: t:z: L; (-rr; ia graotr-rydncua2matpiring ,r :i *lt- 3: l, vi r i;:-lr 1,1 -3:- i2: U.Chrlngt6hartlu,ongthing J, J, ch6o nhau vA viSt phLrong trinh rnAt clr-r nhAn doan vu6ng goc chung cria -\ J, lAm duong kinh D/s: - l, r,,-L,l -: lr HT 165 v6i I toa do Oxyz,clto d r'ong tlrang Trong kh6ng gian v&i h6 toa d6 Oxyz, cho... (r - ir2 - ,,tj -21- i.; - 3ll : 50 i I i i HT 166, Trong kh6ng gian vdi h6 toa dd Oxyz, cho duong thing - * i at I i tnan d cit mit c)u (!J, c6 tAm M, tai hai didm A, B sao I>ti rrnr rrA niy n:rrrrrfirr cho AR n'i.' : cF 6 : : vidr ,,jt - _: : : v) didm 11 i: t:ri,, trinh cia mit ciu Duong I ISJ I D/s: fSJ: -U-\2 -(z- (:i!:ts {.c*7)2 Trong kh6ng gian v6i hC toA d6 Oxyz, cho mAt phdng (d 2r * y - 2:... [S) qua mAt phing i1i ' E/s: (S'l : i:r - 3.i HT HT - g) -:- ::.1 :2it 168 Trong kh6ng gian rr6i hA toa do Oxyz,)Ap phuong trinh mat chu [S] biSt ring mit [P]: : : 2 lhn luot cit ISJ theo hai dr.rong tron cd bdn kinh blng 2 vi B D/* (S): it: - o1! -:y - tt,2 -,r - 1U,1 : 261) (a, b e R) phing Oxy vi mit phang 169 Trong khdng gian vdi hO toa do Oxyz, cYLo mit phing [P]: 2.,: - rt - 2: I - U v) duong... '-ltl - l: - ill '{Nt' tren mat ph.lng t, '= l; -\ i- 1rh I lri d: Trong kh6ng gian voi h0 toa do Ox1,z, cho dulng thing -31 t t : +) :; va m5t phdng [P): 2r-:,rr*)t.-2:0.LApphr-rongtrinhmitcAu[SJcritAn.rnarltr6nducrngthingdc6binkinhnh6nhAttielpxirc ** J vi di qua didrn A[1; -1; 1J [PJ D/s: (:r - 1): * (v - t;2 - :2 : 1 vdi ' HT173 Trongkh6lggranQx;,z,choduongthinsd: ) " b 1-''-'2::v)matpheng[P]: 2t:-... ViSt phuong dr rti - - l')2 - :i i' : 2;! n]r l) doan 1 rlrarla tv: l- -2 r d., tt - 1 -1 0,,1; 2 '2 -r O +r' :;,-'' - DS: l.-+]' *[r*fJ' -f,-il' (s) [' :' - lJ*l _: l::-2 ', (dz) 2 ) y-4 1 163 Trong kh6ng gian vryi hA tQa d6 : : 0 2 (r , -2):' ,'2 +i,{ - -il') -,, - ,t,' l , - 5 z-'2 DS: (,e) , HT kf i, I a) minh Chr?ng cia (.u i t la r lA Vi6tphuongtrinhmitclutAmlvltidpxricvdi truc toa d6 Oxyz,... I - U v) duong thang d: I 'u'ri t-l.Vietphrrcrngtnnhmatcau [S) cirtAm lt].rr-r6cd, IcAch [P] m6tkhodngbing2vA [P] cit[SJ *) - 2 1 theo nrdt dr.rong tron [CJ crj bAn kfnh bing 3 a' H't 170 Tror:g khdng gian vri'i h6 toa dd Oxyz, ch) Z dieim,\i0; tl; al, Bf 2; 0; 0l LAp pirLrgng tr)nh nrat cAir ISJ di qLra O, r\, B r.a co l ... vulng goc v1i (P) = (U, Bx + 7x + i1'z - 46 = HT117 Trongkh6nggianvoihEtructoadij iD) HT ', = (P) 118 Q) suy phLrcrng trinh {D) Trong kh6ng gian vdi hC toa d6 Oxyz, vidt phrrong trinh hinh chi6u... hai duong thang Trong kir6ng gian vor h0 toa dd Oxyz, vidt phuong trinh {wcrng vu6ng Ir:3=ii I , al6n hai ducrng I -1 ,: l, L, vd J.) - -l ,/ l::1-:rt D/st HT130 Trongkhonggianvoi h0toa ddAxyz,vidtphuongtrinhduongthingddiquadidm... ' vIfT pHrroNG TRiNH rvrAr cAu HT161 Trongkh6nggianvdi h0toad6 Oxyz,chodr6m lL; -2: ) Oy E/s: (:r: _ i,2 -iy *212 - (: - j2 : l0 HT 162 r ri, : Trong kh6ng gian vdi f,:zt [r: : t vA d, : : : [