Hình học 11 phần 2 trần văn hạo (tổng chủ biên)

VECTO TRONG KHONG GIAN QUAN HE VUDNG GOC TRONG KH6NG GIAN • ; ' • • • I I I-I 1111 II C* Vectd khong gian *t* Hai dudng thing vuong goc *t* Dudng thang vuong gdc vdi mdt phang *** Hai mat phang vuong goc *t* Khoang each •: * • 11 ' ^ ,.^.r.P^E ^^B^^m -^^< •i Jfc,*'"''' -.^ m -—''^^^ Trong chuong chung ta se nghien cufu ve vecto I AB' SB a) Chiing minh BCl(SOF)=i>(SBC)l(SOF) b) d(0, (SBC)) = ; 0H=^; d(A,(SBC)) = d(I,(SBC)) = IK = 20H=^4 a) Ta ehiing minh BA (ADC) => tam gidc BAD vudng tai A Diing dinh If ba dudng vudng gdc ta ehiing minh BDC Id tam giac vudng tai D 133 b) Chiing minh tam giac AKD cdn tai K vd suy KI ± AD Chiing minh tam gidc IBC cdn tai / vd suy IK BC Do dd IK la doan vudng gde eua AD vd BC BC'IB'C] a) , , l^BC'l(A'B'CD) BC'IA'B'J b) Doan vudng gde chung cua AB' vd BC la KI =—• a) d(S, (ABCD)) = SH= ^ ^ 2-Jl SC = e) Chiing minh A", B", C", Aj', Bj,Cj Cling thude dudng trdn (Oj) Sau dd chiing minh A', B', C ciing thude dudng trdn (Oj) Chdng han, chiing minh 0^\=0^A' a) Gpi (d) = (ES, EM), (d) cdt (SAC) vd (SBD) theo giao tuydn Id dudng thing SO vdi O = AC n BD b)SE = (SAD) n(SBC) c) Goi O' = AC n BD' Chiing minh O'e S0 = (SAC) n (SBD) Chiing minh tii gidc MNFE Id hinh binh hdnh - (EFB) n ^ = ABIF vdi FIII AB b) Vi SH (ABCD) vdi // e AC ndn (SAC) (ABCD) - (EEC) r\S^ = ECFH vdi CF II EH c) Vi SB^ + BC^ = SC^ ndn SB ± BC d) tanc? = - (EEC) nS^ = EMC'FL vdi EM II EC wkFLIICM - Thidt didn tao bdi (EFK) vd hinh ldp phuong Id hinh luc gidc diu = V5 HO BAITAPONTAPCUOINAM Gpi tam gidc A'B'C Id anh cua tam gidc ABC qua cdc phdp bidn hinh trdn, dd a)A'(3;2),B'(2;4).C(4;5); b)A'(l;-l),B'(0;-3),C(2;-4); c)A'(3;l),B'(4;-l),C'(2;-2); d)A'(-l;l),B'(-3;0),C'(-4;2); e)A'(2;-2),B'(0;-6),C'(4;-8) a) F Id phdp vi tu tdm G, ti sd — • b) Dl S ring Id true tdm ciia tam gidc A'B'C c) F(0) = Ol Id trung dilm ciia OH d) Anh ciia A, B,C, A^, B^, Cj qua phdp vi tu tdm // ti sd - tuong ling Id A", B", C , A , 134 DJ , C, Gpi Sly Id hinh ldp phuang a) Gpi / Id tdm hinh vudng BCC'B' Ve IK i BD' tai K IK Id dudng vudng gdc chung ciia BD'vd B'C b)KI=^7 a) Sir dung dinh If ba dudng vudng gdc b) Chiing minh AD', AC vd AB ciing vudng gdc vdi SD c) C D ' ludn di qua / vdi / = AB n CD BANG THUAT NGUT B Bieu thiic toa dp cOa phep tjnh tien Bleu thiic toa dp cCia phep ddi xCrng qua gdc toa dp Bilu thiic tea dp cCia phep ddi xiing qua toic Bong tuydt Von Kdc 41 C Cdc tfnh chdt thC/a nhdn 46 DI3n tich hinh chieu cCia mdt da giac 107 Djnh If ba dudng vudng goc oinh If Ta-let Dudng thing vudng gdc v6i mat phlng Dudng vudng goc chung cCia hai dudng thing cheo 102 68 G Giao tuydn Gdc giufa dudng thing vd mat phlng Gdc giiia hai dudng thing Gdc giiia hai mat phlng Gdc giiia hai vectd khdng gian H Hai dudng thing cheo Hai dudng thing song song Hai dudng thing vudng gdc Hai mat phlng song song Hai mat phlng vudng gdc Hinh bdng Hinh bilu diin Hinh chiiu song song Hinh ehdp Hinh ehdp cijt Hinh ddng dang Hinh hoc i