Thiết kế bài giảng hình học 10 nâng cao (tập 2) phần 2

Chi/ONq III FHl/CiWCS P I I A P 1X)A 1>0 l l l O K G l i H O ^ G GlAN I'huu Gidl THIEU CHLfdNG CAU TAO CHUONG §1 He toa dp khong gian § Phuang trinh mat phdng §3 Phuang trinh dudng thang khdng gian On tap chuang III On tap cuoi nam Muc dich ciia chuong • Chuang III nhdm cung cap cho hpc sinh nhirng kiln thiic co ban vl khai niem toa dp khong gian va nhirng ling dung ciia nd Tpa dp vecto va tpa dp dilm Bilu thirc tpa dp ciia cac phep toan vecto Tich vo hudng ciia hai vecto Phuang trinh mat cau • Gidi thieu vl phuang trinh mat phdng khdng gian Vecto phap tuyen ciia mat phdng - Piiuong trinh tdng quat ciia mat phdng - Dilu kien de hai mat phdng song song, vuong gdc Khoang each tir mot dilm din mot mat phdng • Phuang trinh dudng thdng khong gian: 66 Phuong trinh tham sd ciia dudng thdng - Dilu kien dl hai dudng thang song song - Dilu kien dl hai dudng thdng cheo - Dilu kien dl hai dudng thdng cdt II- MUC TIEU Kien thirc Ndm dupe toan bp kiln thirc co ban chuang da neu tren = Hieu cac khai niem va tinh chat vecto khong gian Hiiu va bilt dupe mdi quan he giira vecto phap tuyIn va cap vecto chi phuang ciia mat phdng Hiiu va bilt dupe mdi quan he giira vecto phap tuylh va vecto ciM phuong ciia dudng thdng KT nang Xac dinh dupe cac vecto khdng gian Van dung dupe eac tinh chat dl giai bai tap - Chiing minh dupe hai mat phang song song, vuong gdc - Lap dupe cac phuong trinh dudng thdng va phuong trinh mat phdng - Xac dinh dupe vi trf tuong ddi ciia dudng thdng va mat phdng, giiia hai mat phdng Thai Hpc xong chuang hpc sinh se lien he dupe vdi nhilu van de thuc t l sinh dong, lien he duoc vdi nhirng van dl hinh hpc da hpc d Idp dudi, md mot each nhin mdi vl hinh hpc Tir dd, cac em cd thi tu minh sang tao nhiing bai toan hoac nhirng dang toan mdi Kit luan: Khi hpc xong chupng hpc sinh cdn lam tdt cac bai tap sach giao khoa va lam dupe cac bai kilm tra chuong 67 P h ^ n 2, CkC BAI SOAN §1 He toa khong gian (tiet 1, 2, 3, 4, 5) MUC TIEU Kien thiic HS ndm dupfc: Khai niem toa dp vecto khdng gian, toa dp dilm va dp dai vecta Bilu thiie toa dp ciia cac phep toan : cdng, trir vecto; nhan vecto vdi mdt sd thuc Bilu thiic toa dp ciia tfch vo hudng ciia hai vecto Phuang trinh mat cdu KT nang • Thuc hien thao cac phep toan vl vecto, tfnh dp dai vecto, • Viet dupe phuong trinh mat cdu Thai • Lien he dupe vdi nhilu van dl thuc t l khdng gian • Cd nhilu sang tao hinh hpc • Hiing thii hpc tap, tfch cue phat huy tfnh dpc lap hoc tap 11 CHUAN DI CUA GV VA HS Chuan bi ciia GV: • Hinh ve 56 din 62 • Thudc ke, phan mau, 68 Chuan bi cua HS : Dpc bai trudc d nha, cd thi lien he vdi phuong phap he tpa dp mat phdng ID PHAN PHOI THOI LUONG Bai dupe chia tilt : Tilt 1: Ttr dau den hit muc Tilt 2: Tilp theo din hit muc Tilt 3: Tilp theo din hit muc Tilt 4: Tilp theo din hit muc Tilt 5: Tilp theo din hit muc IV TIENTOINHDAY HOC n DRT VAN D€ Cau hoi Nhdc lai khai niem hinh hop, hinh chdp Cau hdi Cho hinh lap phuong ABCDA'B'CD' a) Chiing minh eac canh ciia hinh lap phuang xuat phat tir mot dinh vudng gdc vdi b) Cho canh cua hinh lap phuang la a, tfnh dp dai dudng cheo ciia hinh lap phuong a ani MOI HOATDONCl He true tpa khdng gian 69 GV mo ta he true tpa dp khong gian va neu eau hdi : HI Hai vecta i, j co vuong gdc vdi hay khong? H2 Vecto k co vuong gdc vdi tat ca cac vecta thuoc mat phdng (Oxy) khong? • GV neu dinh nghia: He gdm ba true Ox, Oy, Oz doi mdl vudng gdc dugc ggi Id he true tog vudng gdc khdng gian • GV sir dung hinh 56 SGK va dat van dl: H3 Hay dpc ten cac mat phdng tpa dp H4 Hay kl ten cac vecta don vi H5 Cd the cd them mot gdc tpa dp nira khac O hay khong? H6 Hay neu cac tfnh chat ciia mat phdng tpa dp, vecta don vi? -2 — H7 Tfnh i = i.i -2 — -2 j = j.j k = k.k H8.Tfnn i.j,j.k, k.i • Thuc hien | ? l | phiit Hoat ddng ciia HS Hoat ddng cua GV Cdu hdi Tai / Ggi y trd Idi cdu hdi ~ j =k - I Do tinh chat ciia tfch vd hudng ciia cac vecto cimg phuong va cd dp dai bdng Cdu hdi Taisaoi j ^ i k = k i = Ggi y trd loi cdu hdi Do tfnh chat ciia tfch vd hudng ciia cac vecto vuong gdc 70 HOATDONC 2 Toa cua vecto • GV neu dinh nghia : Trong khdng gian cho vecta a Bd ba so (x y :) thda man a = x.i + y.j + z.k ggi la tga ciia vecia a Ki hieu a(x;y;z) hoac a = (x;y;z) H9 Hay tim tpa dp ciia cac vecto i, j , k • Thuc hien ?2 phiit Hoat ddng ciia GV Cdu hdi Tfnh / u Cdu hdi Tfnh u.j Hoat ddng cua HS Ggi y trd Idi cdu hdi ((./ = (xi + yj + :k).i ~ xi - x Ggi y trd Idi cdu hdi HS tu tfnh ' Thuc hien vf du 5' GV sit dung hinh 57 Hoat ddng cua GV Cdu hdi Hoat ddng ciia HS Ggi y trd Idi cdu hdi Bilu diln OM theo cac vecto OM=-(c)J + OK) don vi ^ - I T = 0/+— ; + —A:, Cdu hdi Xac dinh tpa dp ciia OM Cdu hdi Ggi y trd Idi cdu hdi 1 ^ OM = 0; V 2ij Ggi y trd loi cdu hdi Bilu diln MG theo cac vecto MG ^OG-()M, don vi J _l_ V2) (I /+ 3 Cdu hdi J+ k Ggi y trd Idi cdu hdi Xac dinh toa cua MG HS tu viet • GV neu eac tfnh chat ciia tpa dp vecto : Cho cdc vecta i(| = ( X | ; y, ; 2,), /i, =(A-2 ; ^2 ' - ) '''^' ^^'•'' ^ '">' ^'' ta cd : 1) ii, = fh xj = X2, yi = y2, 'i = '2 2) » , + / Y = ( x , + J r ; y | + y ; , + Z ) ij "i-»2=(-^i ^2;>'i->'2;zi 2) 4) kfi^ = ikxi; kyi; kz^) 5) 11^ 112 =X^X2+ >•]^2 + z,Z2 6ihhv^=V^f+>-?+zf 7) cos(/ ()M.k = la M = (x ; y ; 0) 7* ^ .-::l.^;;:: ^:::l ;::;.fi^;::: Hoat ddng cua HS Hoat ddng cua GV Ggi y trd Idi cdu hdi Cdu hdi Tim toa dp eiia A, B, C, D va E Cdu hdi Xac dinh P A = (2 ; 0; 0) Cac dilm khac HS tu lam Ggi y trd Idi cdu hoi HS tu xac dinh HOATDONC 4 Lien he gi&a toa cua vecto va toa cua hai diem mut • GV neu dinh nghia : Cho hai diem A(x^ ; JA ' ^/l) "^^ ^i^B > >'B' ^B)74 1) AB = (xg - x ^ ; J5-^'/i; 2fi-z^) 2) AB ^ Mx, -x^f ' Thuc hien f \ +{yB-yA)'+[-B-^^A) phiit a) Hoat ddng ciia GV Cdu hdi Hoat ddng ciia HS Ggi y trd Idi cdu hdi Neu cdng thiic vecto vl trung 07 = ^ ( A + 0fi) dilm I ciia AB Ggi y trd Idi cdu hdi Cdu hdi Tim tpa dp ciia I y/ = 2\yA + yB)^ 2/ = ^ - ^ ^ - " ) • b) Hoat ddng cua GV Cdu hdi Neu cdng thii'c vecta vl trpng tam Hoat ddng cua HS Ggi y trd loi cdu hdi OG = ^{OA + '0B + 0C^ G ciia tam giac ABC Cdu hoi Ggi y trd Idi cdu hdi Tim tpa dp ciia G -VG = 3(>'-4 +yB + yc); c) Hoat ddng ciia GV Cdu hdi Neu cong thiic vecto vl trpng tam Hoat ddng ciia HS Ggi y trd Idi cdu hdi ~0E ^ ^(7)A+ '0B+ ~0C+ ~0D^ 75 Trd Idi a b c d D D D S Cdu 58 Cho hinh lap phuang ABCDA'BC'D' canh a B' /I A' c / D' ; / (a) Thi tich khd'i lap phuong la a' D (b) The tfch khdi chdp A'.DD'C la - a ' D (c) The tfch khdi lang tru AA'B'.DD'C la - a ' ' D (d) Ca ba cau tren diu sai D Trd Idi a b c d D D D CA) Cdu 59 Cho hai dilm A(0 ; ; 0), B (1, 0, 1) (a) AB =(1 ; - l ;1) D (b) AB = • (c) AB = V3 (d) Ca ba cau tren diu sai D D Trd Idi 183 a b c d D S D S Cdu 60 Cho hai dilm A(0 ; ; 0), B (1, 0, 1) x=t (a) Phuang trinh dudng thang AB la y = l-t D z=t x = l +t (b) Phuang trinh dudng thdng AB la D y = -t z = l +t (c) Phuong trinh dudng thdng AB la x-1 y _ z-1 -1~ (d) Ca ba cau tren diu sai D D Trd Idi a b c d D D D S Cdu 61 Cho phuang trinh x^ +y^ +z^ - 2x +4y 2z = (a) Day la mot phuong trinh mat cdu • (b) Day la mot phuong trinh mat cau tam I (1 ; -2 ; 1) D D D (e) Day la mdt phuang trinh mat cdu cd ban kfnh r = (d) Day la mdt phuang trinh mat cdu ban kfnh r = V6 Trd Idi a b c d D D S D Cdu 62 Cho hinh vudng cd canh la nhu hinh ve 184 D y x=0 (a) Dudng thdng A'D' cd phuang trinh y=t D z=l x=l (b) Dudng thang CC'cd phuong trinh y=l D z=t x =t (c) Dudng thdng A'C'cd phuang trinh y=t D z=l (d) Ca ba cau tren diu sai D Trd Idi a b c d D D D S /// CAU HOI DA LUA CHON Chgn cdu trd Idi dung cdc bdi tap sau: Cdu 64 Cho hinh chdp SABCD, day ABCD la hinh thang vuong tai A, SA ±(ABCD), SA = a, AB = 2a, AD = DC = a Khoang each tir A din (SBC) la 185 (a) a; (e) aV3 ; Trd Idi (d) Cdu 65 Cho hinh chdp SABCD, day ABCD la hinh vudng canh a, SA l(ABCD), SA = a Khoang each giiia AB va SD la (a) a; (c) aV2 ; Trd Idi (d) Cdu 66 Cho hinh chdp SABCD, day ABCD la hinh thang vuong tai A, SA l(ABCD), SA =*a, AB = 2a, AD = DC = a Khoang each tii A din mat phang (SBC) la 186 (a) a'; (c) a^V2 (d) i^Ve Trd Idi (d) Cdu 67 Cho hinh lang tru luc giac diu canh day la 2v3 ndi tiep mot hinh tru cd dudng cao la A' B' C F' Dudng sinh cua hinh tru la : (a)2V3; (b)3V3 (c) ; (d) Trdldi (c) Cdu 68 Mdt hinh cdu cd dudng trdn Idn ngoai tiep mdt tam giac diu canh cd dien tfch toan phdn la : 187 (a)2V3; (b)3V3 (c)^; (d) 67t V3 Trdldi (c) Cdu 69 Gpi d la khoang each tir O cua mat cdu S(0 ; r) den mat phdng (P) Diln vao chd trdng sau : d r 4 Vi tri tuang ddi ciia (P) vd (S) Cdu 70 Cho ba diem 7W(l;0;0), V ( ; - ; ) , B(0;0;l) Nlu MNPQ la mdt hinh binh hanh thi PQ cd phuong trinh la x =t (a)< y = 2t; (c) (b) y=t z=l z=l 'x = l x=t y = 2t ; z =t Trd Idi (a) 188 x = 2t (d) y = 2t z = -l CdM 7/ Cho ba dilm A{\;2;0), B(l;0;-l), C(0;-l;2) Dp dai AB la : (a) 2; (b) (c)l; (d)V5 Trd Idi (d) Cdu 72 Cho ba dilm A{\\2;0), B(l;0;-l),-C(0;-l;2) Dp dai BC la : (a) 2; ''(b) v n (c)l; (d)V5 Trd Idi (b) Cdu 73 Cho tam giac ABC cd ^ = ( l ; l ; l ) , B = ( ; - ; ) , C = ( ; l ; ) Phuong trinh mat phang (ABC) la (a) 3x + y +3z +7 = (b) 3x + y +3z -7 = (c) 3x + y +3z +5 = 0; (d) 3x + y +3z - = Trd Idi (b) CAM 74 Cho tam giac ABC cd ^ = (l; 1; l ) , B = ( ; - ; 3), C = (2; 1; ) Phuang trinh mat phang di qua M (1 ; ; -7) va song song vdi mat phang (ABC) la (a) 3x + y +3z +12 = (b) 3x + y +3z -32 = (c)3x + y+3z+16 = 0; (d) 3x + y+3z - 22 = Trd Idi (c) Cdu 75 Cho tam giac ABC cd J = ( l ; l ; l ) , B = ( ; - ; ) , C = ( ; l ; ) Phuang trinh dudng thang di qua M (1 ; ; -7) va vudng gdc vdi mat phdng (ABC) la 'x = l - t (a)^y = + t z = - + 2t fx = l + 3t (b)jy = - t z = - + 2t 189 X = + 3t (c) x = l + 3t y=2+t (d) z = + 2t y = 2+t z = - + 2t Trd Idi (d) CdM 76 Cho tam giac ABC ed = ( l ; l ; l ) , B = ( ; - ; ) , C = ( ; l ; ) Mat cdu tam / ( l ; l ; - l ) tilp xiic vdi mat phdng toa dp (^ABC) cd phuang trinh la : / \2 / ,\2 ( a ) ( x - l ) + ( y - l ) ' + ( z + l) (b)(x-l)'+(y-l)'+(z-l) 36 19 36 19 (C)(x + l ) + ( y - l ) ^ ( z + l ) ^ (d)(x-l)^(y-l)2+(z + l f = - ^ Trd Idi ia) HOATDONC 2 Hirdng dan tra Idi cau hoi va bai tap on tap cuoi nam Bail 190 a) Hirdng ddn Su dung tfnh chat ciia phep biln hinh HS tu chirng minh b) Hirdng ddn V/^g^ XB'C = ^PQR.P'Q'R' = ^-^^ HS tu chiing minh Bai A / I l \ I I * D ^^ \ / ^ y^ \ , A'V^ ^ •-P/ "v y^ -A -N^ - Hudng ddn phep vi tu tam G vdi ti sd ^ = - - biln tii dien ABCD tii dien A'B'C'D' Bdi vay V^.^'CB' = F I K^BCD = 27 ^ Bai Hudng ddn V V Ddpsd V^cB-D' = ^ " - ^ = y Bai 19] HS tu chiing minh theo hinh ve Ddp sd V^pi^Qs^ =V-4.~ = - Bai HS tu chiing minh Ddp sd V = V,-V^ = 1;,^3 _ I / ^ ^ ^ ^3 -^ J Bai Hudng ddn HS tu ve hinh a) HS tu giai a43 - ^V3^^ Ddp sd 1/ = 71^~^^' a + 2.-n -^^na V b) 1/ = J iSna^ 12 Bai a) Hudng ddn HS tu ve hinh va chiing minh b) Ddp sd d = Bai Hudng ddn a) Hudng ddn Su dung tfch vo hudng \JB,'AC b) Ddp sd X- + y2 + z2 - 2x - 4y + 2z - 19 = c) n 192 = AB.AC (12;-20;12) AD Ddp sd 3x - 5y + 3z + 13 = ; /? = |3.1-5.2 + 3.41 V32+52+32 d) HStu giai Bai Hirdng ddn a) Hudng ddn Viet phuang trinh mat phdng (a) di qua A va vuong gdc vdi mdi mat phang d = (a) giao vdi cac mat phdng tpa dp b) HS tu chiing minh c) Ih = Ill I \' ^/5 |3 I 3V1O V32 + l2 10 = ^ ^ ' +2 /,3 = 1-3 I 3V13 732 + 22 13 12 + 41 ^ = -26 12 d) HS tu giai Ddp sd ^ - - ' ^ - - ^ ' X - e) HS tu giai Ddp sd y = z = / Bai 10 a) Hudng ddn = « ( l - x ) + ( - l - y ) + ( - z ) - ( - x ) - y - ( l - z ) =2 Ddp sd 2x + 2y - 2z - = MA2-MB2 b) Hudng ddn HS tu giai tuong tu cau a) Ddp sd N thudc mat cdu cd tam / ' ' 2j ban kfnh -;r- c) Hudng ddn HS tu giai tuong tu cau a) Ddp sd -X + 3y + (2 + Vl4)z = 193 Bai 11 Bai 10 a) Hudng ddn HS tu giai X = at Ddp sd iy = bt z = + ct b) Hirdng ddn HS tu giai tuang tu cau a) Ddp sd Quy tfch M zl thay ddi la dudng trdn tam O ban kfnh bdng va ndm mat phdng OAy Bai 12 Hudng ddn Chpn he true toa dp nhu hinh ve abc a) Dap so d /ZTTIT Va2 Va2fo2 + &2^2 ^ ^2^2 fe2+^2 ia b AC,CD ^2i,2 , ^ b) Ddp sd h CD a) Hudng ddn h yfJ7, \[BC',CD'].BC\ \[BC' Ddp so , ^2 +b c +c a CD'~\\ abc CAC CAU H | T R A C N G H I E M HS TU GIAI VA TRA LCJI 194 JVIUC LUC Chuang II - MAT CAU, MAT TRU, MAT NON Phdnl Trang Gldl THIEU CHUONG Phdn - c A c BAI SOAN §3 Mat tru, hinh tru, khoi tru §4 Mat non, hinh non, khoi non 21 On top chuang II "* Mot so cau hoi on tap hgc ki mgt Chuong HI - PHUONG PHAP TOA'DQ BM'z i - GIOI THIEU CHUONG 39 49 TRONG KHONG GIAN 66 Phdn - CAC BAI SOAN §1 He tgo khong gian 68 §2 Phucfng trinh mat mat phang 94 §3 Phuang trinh duang thang 116 On tap chuang III 140 On tap chuang cuoi ndm 167 195 Thiet ke bai giang HINH H0C12 - TAP HAI (NANG CAO) TRAN VINH N H A XUAT BAN H A NOI Chiu trdch nhiem xudt bdn: NGUYEN KHAC OANH Bien tap: PHAM QUOC TUAN Vebia: NGUYfiN TUAN Trinh bdy: QUYNH TRANG Siia bdn in: PHAM QUOC TUAN In 1000 cud'n, khd 17x24 cm, taifipng ty TNHH in Ha Anh Giay phep xudt ban sd: 68 - 200^gJ|p/67a TK - 06/HN In xong va nop luu chieu nam 2009 Sach lien ket v6i Cong ty CO phan In va Phat hanh sach Viet Nam P INPHAVI Phat hanh tai Cong ty co phan In va Phat hanh sach Vi( Dia chi : 78 - Dong Cac • Dong Da - Ha Noi OT '041 511 5921 - Fax- (04) 511 5921 ™°i • lllllllllli ^ « !!;n27ll6 G 3" 26.000 O Gic'i: 26.000d [...]... y, 2) u^+ ^2= {x^+x2•,y^+y2\Zl+h) 3) «, - « 2 = ( x , - X 2 ; y, - ^2= Zi -Z2) 4) kui = (kxi ; ky^ ; fe,) 5) Mj.r ' - ^ 2 ' 2 ~ ' ^2) - Cdu hdi 2 Vilt phuong trinh mat cdu Ggi y trd Idi cdu hoi 2 {x-a^){x-a2) + + (z-c,)(z-c -2) = 0 • Thuc hien ^ C 6 trong 5 phiit 82 {y-b^){y-b2) Cdch 1 Hoat ddng cua HS Hoat ddng ciia... (x-Xo )2+ (y-yo )2+ (z-Zo)^=/?^ • GV hudng ddn HS chimg minh dinh If tren • Thuc hien trong ^ 5 phiit Cdch I Hoat ddng ciia HS Hoat ddng cua GV Ggi y trd Idi cdu hdi 1 Cdu hdi 1 Tam I cua mat cau d dau ? Cdu hdi 2 I la trung dilm AjAj Ggi y trd led cdu hoi 2 Tim tpa dp I Cdu hdi 3 fa^+a2 h+b2,c^+C2 /= ^ 2 ' 2 ' 2 ] j Ggi y trd Idi cdu hdi 3 Vilt phuong trinh mat cau R = \A,A2 1 i(ai-a2f+(bi-b2f+(ci-C2f ~2. .. HS tU tfnh Bai 12 a) Hirdng ddn HS tu ve hinh va tfnh b) Hirdng ddn JlNSB = 0 Bai 13 Hirdng ddn HS tu giai a) Mat cdu cd tam /(4 ; - 1 ; 0) va cd ban kfnh 5^ b) Mat cau cd tam / e) Mat cdu cd tam / R^4 7V6 va cd ban kfnh R = :— ;-i;0 va cd ban kfnh R- I Bai 14 Hudng ddn HS tu giai a) x2 + (y - 7 )2 + (z - 5 )2 = 26 b) x2 + iy- 7 )2 + (z - 5 )2 = 26 c) (X-1 )2 + (y - 2) 2 + ( z - 3 ) 2 = 1 2 Phu'cfng t r... Ggi y trd Idi cdu hdi 2 Cdu hdi 2 Tfnh IA, IB,IC va ID va tim cac mdi quan he ciia x, y va z x^ + y^ + z^ = (x - 1 )2 + y^ + z^ ' x^ + y^ +z^ =x^ +(y- 1 )2 + z^ ^2 + y2 + z^ = X^ + y2 + ^ _ lj2 Cdu hdi 3 Vilt phuang trinh mat cdu Ggi y trd Idi cdu hdi 3 HS tu vilt H 22 Hay neu mdt dang khac ciia phuang trinh mat cdu • GV neu nhari x l t : 83 Phuang trinh x^ + y' + z^ + 2ax + 2by + 2cz + d = 0 Id phuang... -2xy trinh mat cau hay khdng ? Ggi y trd Idi cdu hdi 4 Cdu hdi 4 Phuang trinh d) cd la phuong trinh mat cdu hay khdng ? 7 2 ' Phuong trinh nit gpn thanh x +y + z" = 1 Dd la phuong trinh mat cau vdi tam (0; 0; 0) va ban kfnh bdng 1 HOATDONC 7 TOM TfiT Bfil HOC 1 Cho cac vecto w, =(X|; y, ; z,), ta cd : 1) (7, = 1 /2 xj = X2, y, = y2, z^ = z^ 84 "3 ^ (- ^2 ' 3 '2 ' ^2) ^^ so k tuy y, 2) u^+ ^2= {x^+x2•,y^+y2\Zl+h)... Bai 2 Hirdng ddn Dua vao tfnh chat chat ciia gdc giua hai vecto cos (», /) = 2 2 2 2 2 y 2 2 2 ' X + y +z x^ + y'' + z cos (u, k) = , cos (u, j) = 2 X +y'- + z^ HS tu chiing minh tilp Bai 3 Hudng ddn Dua vao tfnh chat ciia gdc giiia hai vecto HS tu giai Bai 4 Hudng ddn Dua vao tinh chat ciia tfch vo hudng hai vecto p i q thi p.q^O Hon nira HS giai tilp = 2, hay (/CM + 1 7 V J ( 3 H - v ) = 0 ;~ - 2; r... 3 Cho a = (l ;2; 3), b = ( - 2 ; 3 ; - l ) Khi dd a + b cd toa dp la (a) a.b = 1 • (b)a.b=-l • (c)2b.a =2 \2 (d) Ca ba khdng dinh tren diu sai [] Trd Idi a b c d D s D S Cdu 4 Cho hinh cau cd phuang trinh : (x -1)^ + (y + 2) ^ + (z + 3)^ = 2 (a) Tam ciia hinh cdu la 1(1 ; -2 ; -3) D (b) Tam cua hinh eau la I(-l ; 2 ; 3) • (c) Ban kfnh ciia hinh cdu la 2 D (d) Ban kfnh ciia hinh cau la \ /2 • Trd Idi a... trd Idi cdu hdi 1 Gpi phuang trinh mat cau cd d^O dang x' + y" + 7^ + 2ax + 2by + 2c: + d - 0, hay tim mdi quan he khi mat cau di qua A Cdu hoi 2 Goi y trd Idi cdu hdi 2 l+2a = 0;l+2b = 0;\+2c =0 Tim mdi quan he khi mat cdu di qua B, C va d Goi y trd Idi cdu hdi 3 Cdu hdi 3 Vilt phuong trinh mat cdu 2 2 ' ^ X +y +z~-x-y-z = 0 Cdch 2 Hoat ddng ciia GV Cdu hdi 1 Hoat ddng ciia HS Ggi y trd Idi cdu hdi... cdu Id r = ^a^ + > 7 2 b^+c^-d 2 H23 d phai thoa man diu kien gi de x + y + z + 2ax + 2by + 2cz + d- = 0 la phuang trinh ciia mat cdu ? 7 trong 5 phiit • Thuc hien ^ Hoat ddng cua HS Hoat ddng ciia GV Ggi y trd Idi cdu hdi 1 Cdu hdi 1 , , , 2 2 ' Phuang trinh a) cd la phuang Khdng phai, vi he sd cua x y va z' trinh mat cdu hay khdng ? khdng bdng nhau Cdu hdi 2 Grn y trd Idi cdu hdi 2 Phuang trinh b) cd ... 1 12 =X^X2+ >•] ^2 + z,Z2 6ihhv^=V^f+>-?+zf 7) cos(/