PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 !" #$%&$'()*+&$*,& /-#$% Oxyz O i j k= = = r r r i j j k k i= = = r r r r r r 0#$%&$)%-'() OM x i y j z k M x y z= + + ⇔ uuuur r r r 1#$%&$)%-*,& a a i a j a k a a a a= + + ⇔ = r r r r r 23456-7 OM x y z M x y z= ⇔ uuuur '(8-9&-#$%&$&:&;6;-<:4*,& 2=4>?7 a a a a b b b b= = r r a b a b a b a b+ = + + + r r a b a b a b a b− = − − − r r ka k a a a ka ka ka= = r k ∈R 2/@8A7 a a a a b b b b= = r r a b a b a b a b = = ⇔ = = r r = r b ≠ r r a r b r !"#$%"& '&()k)** a kb= a kb= a kb= + A A A B B B A x y z B x y z B A B A B A AB OB OA x x y y z z= − = − − − uuur uuur uuur M, -".(/*0"1"AB2 A B A B A B x x y y z z M + + + ÷ ?&*BCD4E '(8-9&-#$%&$-?&*BCD4E 345", a a a a a b a b a b a b b b b b = ⇒ = + + = r r r r 04EFG4E 4+ /(6% a a a a a a a a= ⇒ = + + r r *7"89.( B A B A B A AB AB x x y y z z= = − + − + − uuur :96% *) a b a b a b = r r r r r r HC.4E-IJ4)K-&L8 2=4>?7;<=S>( I a b c 8"&"r?, ( ) ( ) ( ) x a y b z c r− + − + − = 23456-7? x y z ax by cz d+ + − − − + = a b c d+ + − > , ?/(<= >( I a b c 8"&" r a b c d= + + − @ PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 MN A* 6% Ba = − r b = − r Cc = r 2( / 8 6% @ u a b c = − + r r r r B v a b c= − + r r r r 0A*2"# ABCD A B C D ′ ′ ′ ′ D A − B − C − D ′ − 2( 8'"E",0/2"# 12(/ u r D @a u a + = r r r a = − r a u b + = r r r @B a = − r FC b = r a b c u + − − = r r r r r a b c= = − = − r r r + Ba u = − r r b u = − r r c u = r r a = − r b = − r @c = − r 6 a u ⊥ r r b u ⊥ r r Cc u = − r r a = − r b = − r c = − r G a u ⊥ r r b u ⊥ r r u = r a b c= = − = − r r r O-*"&H""Oxyz*.( @FA − B B − − C − AI"("A B C, '"/((8 2(.(D)**ABCD, 2"2" " 2(*.(/$J"K* +2(8.($%"I", >"$J"#>"8-*"$J"#>"8"* /A /LABC 6AI"("OABC, "'"/(I+"2(-">(/I+" PA*".( CA − F B − − C − B CD 2(-">(/ ABC ∆ 2(-">(/I+"ABCD Q-*"&H""Oxyz*8.( ( ) ( ) ( ) A B C− − D Oy∈ "+"/LABC "+ $J"*&MN'"A/LABC 2(/.(D../I+"ABCDO"B +"H)"/9$J"1"OA BC A*2",P##$%" ABCD A B C D ′ ′ ′ ′ M N ,=",$Q, -".(/ AD BB'AI"(" MN A C ′ ⊥ R 2(-R"Oy.(M8S.( A B − 2(-R"(<#1"Oxz.(N8S.( A − @B − C − SA*(8ABCD A − @ B − C − AI"(" ABC ∆ >" T " 0*T 8 <# 0" / I +" ABCD A B C D − − " u v r r D Bu = − r @ Bv = − r ( ) ( ) u v= = − r r 0"&*7"89.(A BD @ A − B ( ) ( ) A B 1"96% a r b r D a = r @b = − r B a = r C b = − r OAI"("(88'" BA − B − − B C − , (8"" PA*(8ABCD CA − F B − − C − "+ 80")U- ABC ∆ H" "R QA*(8ABCD A − B − C − "+ 80" 2(-".(/80" 2(-">( @ Ch 7 Trng THPT Phc Long A*6% a = r b = r 2(/86% a b r r V Wa b b + r r r RA*.( A B C 2(/6% AB AC uur uur SA* ABC A B CB C "+ $J"*0NB 0TA*".( A F B C CD AI"("A B C D, "'"/(I+" "0*T8<#0"/I+" "./I+"ABCD + $J"*/I+"&MN'"A 0 2( + $J" * 0 N '" A / I +" ABCD D A @ B C FC B @XD 002(+ $J"*OH/ OAB D CA @@B 012(+ $J"#>"8-*"&MNB/ ABC D A B @FBC 0O2(>( 8"&"/8(<=? @ Bx y z + + + = @ Bx y z + + + + = @ C @ x y z x y z + + + + = + X x y z z + + = 6 C @ B x y z x y z + + + + = G @ X @ x y z x y z + + + + = C B x y z x y z + + + = 0PYP#?/(<= 4Z.( A >( B A$J"&"AB @ A BB A>( ( ) I D#[\(#Oxy +4Z.( ( ) ( ) A B >(-]Ox 64Z.( ( ) ( ) ( ) B @ A B C >((#Oxz G4Z".( ( ) ( ) ( ) ( ) @ A B C D 0UVWX !" H&$); =44EY$ n r , ^?/ n n r r r giaự cuỷa vuoõng goực vụựi _D )*")*"*<I8/6%&8#$%", a a a a= r b b b b= r 2 (^?, n a b a b a b a b a b a b a b= = r r r 0Z&$); ?/(# Z.( M x y z "P" n A B C= r , (^?, A x x B y y C z z + + = _D Ax By Cz D + + + = 2 (^?, n A B C= r ?/ Z.( A a B b C c abc , x y z a b c + + = 1'8['/4($');\<4E\<4E]*8B4EE^& -*"&H""Oxyz* A x B y C z D + + + = ^? n A B C= r A x B y C z D + + + = ^? n A B C= r // n kn D kD = r r A B C k A B C D kD = n kn D kD = = r r A B C k A B C D kD = = `)*-6`*)`*"6-+*"`+a6(#`+*(6"`*"b"b#bb+6bFbb@@@@X@CB`,X@CBCB+* @ PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 n n α α ⊥ ⇔ = r r A A B B C C⇔ + + = Chú ý: caét n kn α α ⇔ ≠ r r A B C k A B C⇔ ≠ O<A4E&:&-_)%-'()`4)%-); -*"&H""Oxyz&*7"8N.( M x y z D"(# Ax By Cz D α + + + = , Ax By Cz D d M A B C α + + + = + + MN ^D?/(<#1" 4Z.( BM − "P" @n = − r , (^? 4Z.( M − )*")*"(<#1" B x y z+ − + = 4Z.( BM − )*")*"8/6% ( ) ( ) a b= = − r r +4Z.( M − @N )*")*"-]Ox 64Z.( M N − H"(<#1" x y z+ − = G4Z.( ( ) ( ) A B − H"(<#1" x y z− + − = 0^D?/(<#1"Z.( A − BB − C @A − BFB C − − − ( ) ( ) ( ) M N P− − + ( ) ( ) ( ) @ C A B C− 1^D?(<#1"-"-c/*0"MN M − − N − M BCN − OA* ABC∆ BFA − B − C − ^D?/(<#1"Z.(A H" BC P^D?/(<#1" d.( M − I-]Oz 4 Z .( M − H" (< #1" B x y z− + + = B @ x y z− + + = 4 Z .( M − Z * UD" / (< #1" B x y z− + − = B x y z− + − = +d*UD"/(<#1" @ x y+ − = B y z− − = e"JH" (<#1" x y z+ − − = 6d*UD"/(<#1" @ B x y z− + − = @ B y z+ − = e"J)*")*" (<#1" f x y− + = Q A* .( ( ) ( ) A B− − ^D ? / (#P H" AB 8 .( ( ) M − (&*7"O" A*I+"ABCD B A C B B @C @ CD ^D?/(<#1"BCD ^D?/(<#1"gZ.(A B )*")*"CD Rh85"m n. // α β D F x my z α + − − = F C @ nx y z β + − + = B x y mz α − + − = B x ny z β + + − = Sh85"m n. α β ⊥ D F x y mz α − + + = B x y z β + − + = @ x y z α − − = F mx y z β + − − = ThK5-$%"/(<#1" B x y z α + − + = @ X B x y z β + − − = C @ C B x y z α − − + = X B x y z β − − − = @ Chủ đề 7 Trường THPT Phước Long @ B x y z α − − + = B B B x y z β − − + = A*(# B x m y z α − − + − = m x y mz β + − + − = 2(m. `` α β α i β α β ≡ 0YP#?/(<= 4Z.( A − B − − C >("O(-R"(<#1"Oxy 4Z.( ( ) ( ) @ C D− − >($J"1" x t d y t z t = + = + = − − 4Z.( A B − C − >((<#1" @ x y z+ + − = +A>( B I − − D#[\(<#1" x y z− − + = 2(D#.( 6A>( I − D#[\(<#1" @ x y z+ − − = 2(D#.( G A >( -R" $J" 1" x y z d − − − = = − − D# [\ (< #1" P x y z+ − − = @ Q x y z+ − + = A8"&"r = D#[\(<#1" x y z+ + + = 0 M − A>( I − i$J"1" B f x y z d + + + = = − 0.(A B)** CAB = 1hK5-$%"9(<= (<#1"-*"8-$J"Q#) C x y z x y z + + − + − + = x y z+ + = C C x y z x y z + + − + − + = z − = @ @ x y z x y z + + − + − − = B x − = O^D?/(#D#[\(<= @S x y z − + − + + = 0.( M − P^D?/(<#1"D#[\(<= x y z x y z + + − − − − = )*")*" (<#1" C @ x y z− + + = YP#?/(<#1"I$J"1"d @ @ x y z− − − = = D#[\(<= C X x y z x y z + + − + + + = QA*I+"ABCD C A − CB C − @D ^D?D#+" /(<="*0D#I+"ABCD0A YP#?/(#D#[\(<= C S x y z x y z + + − + + − = )*")*" $J"1" B x y z d + − + = = − F X x t d y t z = − + = − − = YP# ? (< #1" I $J" 1" C X x y z d − − − = = D# [\ (< = C B x y z x y z + + + − + − = ^D?/(#P)*")*"OzH" Q x y z+ + = D#[\(<= @ S x y z x y z + + − + − − = R"&*7"8N8.( M − @ M @M − D"(<#1" x y z− + − = "&*7"8ND"(<#1" C P x y z+ − − = SA*I+"ABCD A @ B − CFC B @XD − − "+ $J"*0N A/I+" `)*-6`*)`*"6-+*"`+a6(#`+*(6"`*"b"b#bb+6bFbb@@@@X@CB`,X@CBCB+* @@ PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 1UaX !" b&$- 4$J"1"dZ.( M x y z "P" u a b c= r , (^A??j, x x at y y bt z z ct = + = + = + 4$J"1" d Z.( M x y z "P" u a b c= r abc ≠ , (^A? ?A, x x y y z z a b c − − − = = 0'8['/4($'-\<4E\<4E]-Ic4E4$8]&d-4$8*+&6<4$8 -*"&H""Oxyz* x x at d y y bt z z ct = + = + = + x x a t d y y b t z z c t ′ ′ ′ = + ′ ′ ′ ′ = + ′ ′ ′ = + 4$J"1"dZ.( M x y z ^A? u a b c= r d’Z.( M x y z ′ ′ ′ ′ ^A? u a b c ′ ′ ′ ′ = r hK ? x at x a t y bt y b t I z ct z c t ′ ′ ′ + = + ′ ′ ′ + = + ′ ′ ′ + = + u ku d d M d ′ = ′ ⇔ ′ ∉ r r // u ku d d M d ′ = ′ ≡ ⇔ ′ ∈ r r di d ′ ⇔ kl("( d d ′ K*" u u ′ ⇔ r r kcp vôùi Heä (I) voâ nghieäm d d u u ′ ′ ⊥ ⇔ = r r 1'8['/4(-\<4E\<4E]4e)-I<4E<K&&d-); -*"&H""Oxyz* x x at d y y bt z z ct = + = + = + (# Ax By Cz D α + + + = 4$J"1"dZ.( M x y z ^A? u a b c= r α ^?, n A B C= r hK? A x at B y bt C z ct D+ + + + + + = d α ⇔// ?H"( d α ⊂ ⇔ ?H)"( di α ⇔ ?("( MN ^D?j?A"D/$J"1"d-*"8-$J"Q#) d Z.( M − ^A? Ba = − r d Z.( FA − @B d Z.( @ A )*")*"$J"1" B B @ x y z− − ∆ = = − +d Z.( BM − H"(# @ x y z α − + − = 6d Z.( BA − )*")*"$J"1" B x y t z t = ∆ = − − = + Gd Z.( M )*")*"-]Ox @B Chủ đề 7 Trường THPT Phước Long dZ.( ( ) B − − )*")*"(# P x y z+ − = H"$J"1" x t d y z t = − ′ = = + 0AI"(" d d ⊥ C x t d y t z t = + = − + = − x y z d − + − = = x t d y t z t = − = − = − − x y z d + − = = − 1^D?/$J"1", 2"DH"/$J"1"d-R"(<#1" α x y z d + + − = = B x y z α + − + = X f B x t d y t z t = − − = − + = − − x y z α − + − = O^D?/$J"1"Z.(M H"$J"1" d d M − x t x y z d d y t z t = − − − = = = + − = − BM x t x t d y t d y t z t z t = + = − = − = + = + = − P ^D ? / $J" 1" Z .( ( ) M − H" (< #1" F x y z α − + − = A*(8ABC A B C ^D?j/$J"1" Z-">(/(8ABC H"(<#1"I(8 Q^D?(<#1" α Z.(A H"$J"1"d A x y z d − − = = A − @ x d y t z t = = − = hK5-$%"/8<#$J"1" x t d y t z = + = − + = x d y t z t = ′ ′ = + ′ = − x t d y t z t = − + = − = + x y z d + − ′ = = − B @ x y z d − + − = = C x y z d − + + = = R2()*.([K5-$%"/$J"1"d (<#1"g @ x t d y t z t = − + = + = − x y z α + − + = B f x t d y t z t = + = + = + x y z α − − − = x y z d + − − = = x y z α − − + = S2(*.(/$J"1"d (<#1" α `)*-6`*)`*"6-+*"`+a6(#`+*(6"`*"b"b#bb+6bFbb@@@@X@CB`,X@CBCB+* @C PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 x t d y t z = − + = − − = B x y z α − + − = x t d y t z t = + = − + = − x y z α − + − = T^D?/$J"1"dZ.( M i$J"1" x t d y t z t = − + = − = + x y z d + − = = − ^D?/(<#1"I$J"1" d )*")*"$J"1" d x t d y t z = + = − + = x d y t z t = ′ = + ′ = − @ X @ F B x t d y t z t = + = + = + x t d y t z t ′ = + ′ = − + ′ = + 0^D?$J"H""/$J"1"K*" B x y z d − − + = = @ @ x y z d + − − = = − − @ x d y t z t = = − + = + x t d y t z ′ = ′ = + = − 1 " &*7" 8 N .( S − D" (<#1" P Z .( C FA − BB − @ F C − − jU-./I+"SABC O2(P#Q#8.(8S(<#1" x y z− + + = B x y z− + + = @ X x y z− + + = @ X B x y z− + + = P"&*7"89(<#1" B x y z− + = B x y z− + − = Q-R"-]Oz2(.(8S.( A − (<#1" B x y z+ + − = -R"-]Oy2(.(8S(<#1" x y z+ − + = B x y z− + − = R A*I+" ABCD @A − − @ B − − C − D "+ $J"*0ND/I+" Sk2"#9"P8'" A @ B BC O D , '"+"Oh85"'"D^D?d/(#ABD"&*7"8NC (#ABD 0T"&*7"8N.( A D"$J"1" x y z − − ∆ = = 0A*.( A $J"1" @ x y z− + ∆ = = ^D?(<#1"ZA I ∆ "&*7"8N.(AD"$J"1" ∆ 002(&*7"898<#$J"1")>U x t d y t z = + = − + = x d y t z t = ′ = + ′ = − x y z d + − − = = − B x y z d − + = = − 01"98<#(<#1" x y z+ + − = C B x y z+ − − = C x y z+ − = C x y z+ + − = @F Chủ đề 7 Trường THPT Phước Long 0O"98<#$J"1")>U @ x t d y t z t = + = − + = − + @ x t d y t z t ′ = − + ′ = − ′ = + @ x t d y z t = − + = − = − C x t d y z t ′ = − = ′ = 0P"9$J"1" ∆ (<#1" α -*"8-$J"Q#) x y z + + − ∆ = = B x y z α + − + = x y z + − ∆ = = − x y z α + − + = 0QA*$T"1" x y z+ − − ∆ = = − (# x y z α − + − = 2(*.(A/ ∆ α "9 ∆ α 02(2"DH"/.( A -R"(# C C x y z α + + − = 2(.(Am[I".(AZ(# α 0R2(2"DH"/.( M − − ,R"(# @ @ B x y z α − + − = 2(.(Mm[I".(MZ(# α 0S A*I+" ABCD @@A B BBC D 2(2"D H"/.(D-R"(<#1"ABC ".I+"ABCD 1T2(.([I"/.( M − Z(<#1" x y z− − − = 1 ^D ? / $J" 1" Z .( M H" $J" 1" C x y z d − − − = = − i$J"1" x t d y t z ′ = + ′ = − − = 10 ^D ? $J" 1" H" (<#1" x y z+ + − = i $J" 1" x y z d − + = = − C @ x t d y z t ′ = − = − ′ = + 11A*$J"1" x y z + + − ∆ = = (# B x y z α + − + = ^D?/$J" 1"Z*.(/ ∆ α "O(-*"(<#1" α H" ∆ 1OA*.( A − $J"1" @ x t y t z t = − + ∆ = + = − 2(.(H, 2"DH"/.(A-R"$J"1" ∆ 2(.(Am[I".(AZ ∆ 1PA*$J"1" x y z d − − + = = − (# P x y z+ − − = h85"*.(A/d P ^D?/$J"1" ∆ D ∆ ZA"O(-*"P d ∆ ⊥ `)*-6`*)`*"6-+*"`+a6(#`+*(6"`*"b"b#bb+6bFbb@@@@X@CB`,X@CBCB+* @X . PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 . I a b c 8"&" r a b c d= + + − @ PP tọa độ trong không gian Đề cương ôn tập thi TN THPT năm học 2009-2010 MN A* 6% Ba = − r . 2(-".(/80" 2(-">( @ Ch 7 Trng THPT Phc Long A*6% a = r b = r 2(/86% a b r r V Wa b b + r r r RA*.( A B C 2(/6% AB