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<blockquote data-quote="i love all" data-source="post: 71892" data-attributes="member: 74430">[FONT=.VnTime]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Phư¬ng ph¸p gi¶i h×nh häc gi¶i tÝch trong kh«ng gian [/FONT]&nbsp; [FONT=.VnTime] H×nh häc gi¶i tÝch trong kh«ng gian lu«n cã trong c¸c ®Ò thi vµo ®¹i häc, tèt nghiÖp trung häc phæ th«ng, bµi viÕt nµy lµ tæng hîp c¸c d¹ng cña ®Ò thi. Mong bµi viÕt nµy cã thÓ gióp cho c¸c b¹n cã thÓ häc tèt vµ lµm bµi h×nh häc gi¶i tÝch ®îc tèt h¬n trong c¸c k× thi.A,Lý thuyÕt:[/FONT]&nbsp; [FONT=.VnTime] Quy t¾c h×nh hép[/FONT] [FONT=.VnTime] : ABCDA’B’C’D’ lµ h×nh hép th× : 3 vect¬ ®ång ph¼ng:&nbsp; [/FONT] [FONT=.VnTime] ®ång ph¼ng khi :[/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; HoÆc sao cho [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; HoÆc [/FONT] [FONT=.VnTime] TÝch v« híng cña 2 vect¬: cho [/FONT]&nbsp; [FONT=.VnTime] &nbsp; Ta cã : [/FONT] [FONT=.VnTime] TÝnh chÊt: [/FONT] [FONT=.VnTime] +, cïng ph¬ng [/FONT][FONT=.VnTime][/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +, vµ [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +,&nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +,&nbsp; &nbsp;&nbsp; [/FONT] [FONT=.VnTime] &nbsp;&nbsp; HÖ qu¶:[/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +, [/FONT][FONT=.VnTime][/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +,&nbsp; &nbsp;&nbsp; (diÖn tÝch h×nh b×nh hµnh)[/FONT][FONT=.VnTime][/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +,&nbsp; &nbsp;&nbsp; (thÓ tÝch h×nh hép)[/FONT][FONT=.VnTime][/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +,&nbsp; &nbsp; (thÓ tÝch tø diÖn)[/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +,&nbsp; ®ång ph¼ng [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; kh«ng ®ång ph¼ng [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; +, Gãc cña 2 mÆt ph¼ng : lµ:&nbsp; &nbsp; &nbsp;&nbsp; B, Ph¬ng ph¸p gi¶i:[/FONT]&nbsp; [FONT=.VnTime]&nbsp; I,MÆt ph¼ng:&nbsp; [/FONT] [FONT=.VnTime] &nbsp; PTTQ(ph¬ng tr×nh tæng qu¸t) mÆt ph¼ng(mp) qua vµ cã&nbsp; VTPT(vect¬ ph¸p tuyÕn) lµ: [/FONT]&nbsp; [FONT=.VnTime] &nbsp; &nbsp;&nbsp; hay : víi [/FONT]&nbsp; [FONT=.VnTime] &nbsp; PTMP(ph¬ng tr×nh mÆt ph¼ng) qua cã ph¬ng tr×nh(pt) lµ: [/FONT]&nbsp; [FONT=.VnTime] &nbsp; KÕt qu¶:[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,PTMT to¹ ®é oxy:&nbsp;&nbsp; z=0[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,PTMT to¹ ®é oxz:&nbsp;&nbsp; y=0[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,PTMT to¹ ®é oyz:&nbsp;&nbsp; x=0[/FONT]&nbsp; [FONT=.VnTime]VÞ trÝ t¬ng ®èi cña mÆt th¼ng vµ mÆt ph¼ng:[/FONT]&nbsp;&nbsp; [FONT=.VnTime] Cho Ph¬ng tr×nh chïm mÆt ph¼ng:[/FONT]&nbsp; &nbsp; &nbsp;&nbsp; [FONT=.VnTime]&nbsp;TËp hîp c¸c mÆt ph¼ng chøa ®êng th¼ng&nbsp; ®îc gäi lµ chïm mÆt ph¼ng x¸c ®Þnh bëi mp&nbsp; vµ mp . NÕu&nbsp; vµ&nbsp; th× ph¬ng tr×nh mÆt ph¼ng lµ:[/FONT] [FONT=.VnTime] &nbsp;&nbsp; (*) víi [/FONT] [FONT=.VnTime] ph¬ng tr×nh (*) cã thÓ viÕt l¹i: [/FONT]&nbsp; [FONT=.VnTime] &nbsp; C¸c vÊn ®Ò: ViÕt PTMP(ph¬ng tr×nh mÆt ph¼ng):[/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua vµ cã&nbsp; VTPT [/FONT]</li>
</ol>[FONT=.VnTime] +,X¸c ®Þnh cña mp[/FONT] [FONT=.VnTime] +,X¸c ®Þnh VTPT [/FONT] [FONT=.VnTime] +,¸p dông c«ng thøc : [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua vµ cã&nbsp; cÆp VTCP(vect¬ chØ ph¬ng) [/FONT]</li>
</ol>[FONT=.VnTime] (víi cã gi¸ song song hoÆc n»m trªn mp ) [/FONT] [FONT=.VnTime] +,T×m VTPT [/FONT] [FONT=.VnTime] +, lµ mp qua vµ cã&nbsp; VTPT [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua 3 ®iÓm kh«ng th¼ng hµng A,B,C[/FONT]</li>
</ol>[FONT=.VnTime] +,T×m [/FONT] [FONT=.VnTime] +,T×m VTPT [/FONT] [FONT=.VnTime] +, lµ mp qua A vµ cã VTPT [/FONT] <ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua&nbsp; vµ vu«ng gãc víi 2 mp vµ c¾t nhau[/FONT]</li>
</ol>[FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,T×m VTPT cña vµ lµ vµ [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,T×m VTPT cña [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, lµ mp qua vµ cã&nbsp; VTPT [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua vµ qua giao tuyÕn 2mp c¾t nhau lµ vµ [/FONT]</li>
</ol>[FONT=.VnTime] +, cã d¹ng : (*)&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; víi [/FONT] [FONT=.VnTime] +, qua thÕ vµo ph¬ng tr×nh (*)[/FONT] [FONT=.VnTime] +,Rót ra m theo n chän m,n råi thÕ vµo phong tr×nh (*)[/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua vµ vu«ng gãc víi ®êng th¼ng (d)[/FONT]</li>
</ol>[FONT=.VnTime] +,T×m VTCP cña (d)[/FONT] [FONT=.VnTime] +, lµ mp qua vµ cã&nbsp; VTPT = [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP qua vµ chøa ®êng th¼ng (d)[/FONT]</li>
</ol>[FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; TH1: (d) cã d¹ng tæng qu¸t[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, T×m PTMP ta dïng c«ng thøc chïm mp.[/FONT] [FONT=.VnTime] TH2: (d) cã d¹ng chÝnh t¾c[/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; C¸ch 1:&nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, ChuyÓn ph¬ng tr×nh (d) vÒ d¹ng ph¬ng tr×nh t«ng qu¸t[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,Dïng c«ng thøc chïm mp[/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; C¸ch 2:&nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,T×m vµ cã VTCP&nbsp; cña (d)[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +,T×m [/FONT]&nbsp; [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; +, lµ mp qua vµ cã&nbsp; VTPT&nbsp; [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PTMP chøa ®êng th¼ng vµ // [/FONT]</li>
</ol>[FONT=.VnTime] +,T×m vµ cã VTCP cña [/FONT] [FONT=.VnTime] +,T×m VTCP cña [/FONT] [FONT=.VnTime] +,T×m [/FONT] [FONT=.VnTime] +, lµ mp qua A vµ cã VTPT [/FONT]&nbsp; [FONT=.VnTime]II,§êng th¼ng:[/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; PTTQ(ph¬ng tr×nh tæng qu¸t):&nbsp; [/FONT] [FONT=.VnTime] VTCP(vect¬ chØ ph¬ng): [/FONT] [FONT=.VnTime] §Æc biÖt:[/FONT] [FONT=.VnTime] +,ph¬ng tr×nh trôc ox: [/FONT] [FONT=.VnTime] +,ph¬ng tr×nh trôc oy: [/FONT] [FONT=.VnTime] +,ph¬ng tr×nh trôc oz: [/FONT] [FONT=.VnTime] PTTS(ph¬ng tr×nh tham sè): (d) qua vµ cã VTCP :[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; (d) : [/FONT] [FONT=.VnTime] PTCT(ph¬ng tr×nh chÝnh t¾c): (d) : [/FONT]&nbsp;&nbsp; [FONT=.VnTime]VÞ trÝ t¬ng ®èi cña ®êng th¼ng vµ ®êng ph¼ng:[/FONT]&nbsp; [FONT=.VnTime] Cho&nbsp; qua vµ cã VTCP [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; qua vµ cã VTCP [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; chÐo nhau&nbsp; kh«ng ®ång ph¼ng [/FONT] [FONT=.VnTime] &nbsp;&nbsp; ®ång ph¼ng&nbsp; ®ång ph¼ng [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; ®ång ph¼ng&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; c¾t nhau&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; kh«ng cïng ph¬ng&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [/FONT]&nbsp;&nbsp; [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; cïng ph¬ng&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; song song&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; [/FONT]&nbsp; &nbsp; &nbsp; &nbsp; [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; cïng ph¬ng[/FONT] [FONT=.VnTime] &nbsp;&nbsp; trïng nhau [/FONT]&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; [FONT=.VnTime] &nbsp; &nbsp;&nbsp; Cã&nbsp; &nbsp; &nbsp; &nbsp; víi&nbsp; [/FONT]&nbsp;&nbsp; [FONT=.VnTime] C¸c vÊn ®Ò: ViÕt PT§T(ph¬ng tr×nh ®êng th¼ng)TH1:§êng th¼ng (d) ®îc x¸c ®Þnh bëi 1 ®iÓm vµ 1 VTCP[/FONT] [FONT=.VnTime] 1.&nbsp; &nbsp; &nbsp; [/FONT] [FONT=.VnTime] PT§T (d) qua vµ cã VTCP [/FONT] [FONT=.VnTime] +,Dïng PTTS hay PTCT[/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua vµ (d) song sonh víi 1 ®êng th¼ng cho tríc[/FONT]</li>
</ol>[FONT=.VnTime] +,T×m VTCP cña (d)[/FONT] [FONT=.VnTime] +,(d) lµ ®êng th¼ng quavµ cã VTCP&nbsp;&nbsp; [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua vµ (d) song sonh víi 2 mp c¾t nhau [/FONT]</li>
</ol>[FONT=.VnTime] +,T×m VTPT cña mp : [/FONT] [FONT=.VnTime] &nbsp; &nbsp; T×m VTPT cña mp : [/FONT] [FONT=.VnTime] +,T×m [/FONT] [FONT=.VnTime] +,(d) lµ ®êng th¼ng quavµ cã VTCP&nbsp;&nbsp; [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua vµ [/FONT]</li>
</ol>[FONT=.VnTime] +T×m VTPT cña mp lµ [/FONT] [FONT=.VnTime] +,(d) lµ ®êng th¼ng quavµ cã VTCP =&nbsp; [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua vµ (d) vu«ng gãc víi 2 ®êng th¼ng vµ [/FONT]</li>
</ol>[FONT=.VnTime] +,T×m VTCP cñalµ[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; +,T×m VTCP cñalµ [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Gäi [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; +,(d) lµ ®êng th¼ng quavµ cã VTCP&nbsp; [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua , vµ (d) c¾t [/FONT]</li>
</ol>[FONT=.VnTime] +,LËp PTMP qua vµ [/FONT] [FONT=.VnTime] +,T×m giao ®iÓm N cña vµ[/FONT] [FONT=.VnTime] +,(d) lµ ®êng th¼ng ®i qua 2 ®iÓm vµ N [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua vµ (d) c¾t 2 ®êng th¼ng , cho tríc[/FONT]</li>
</ol>[FONT=.VnTime] &nbsp; C¸ch 1:[/FONT] [FONT=.VnTime] +, LËp PTMP qua vµ[/FONT] [FONT=.VnTime] +,T×m giao ®iÓm N cña vµ[/FONT] [FONT=.VnTime] +,(d) lµ ®êng th¼ng qua ,N[/FONT] [FONT=.VnTime] +,Chøng tá (d) c¾t [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; C¸ch 2:[/FONT]&nbsp; [FONT=.VnTime] +, LËp PTMP qua vµ[/FONT] [FONT=.VnTime] +, LËp PTMP qua vµ[/FONT] [FONT=.VnTime] +,(d) lµ giao tuyÕn cña vµ [/FONT] [FONT=.VnTime] +,Chøng tá (d) c¾t , [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] PT§T (d) qua , vµ (d) c¾t&nbsp;&nbsp; [/FONT]</li>
</ol>[FONT=.VnTime] +,LËp PTMP qua vµ [/FONT] [FONT=.VnTime] +,T×m giao ®iÓm N cña vµ[/FONT] [FONT=.VnTime] +, (d) lµ ®êng th¼ng qua M,NTH2: (d) x¸c ®Þnh lµ giao tuyÕn cña 2 mÆt ph¼ng:[/FONT] <ol>
<li data-xf-list-type="ol">[FONT=.VnTime] Ph¬ng tr×nh ®êng vu«ng gãc chung cña 2 ®êng th¼ng chÐo nhau vµ [/FONT]</li>
</ol>[FONT=.VnTime] +,Trong kh«ng gian cho 2 ®êng th¼ng chÐo nhau:[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; qua vµ cã VTCP [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; qua vµ cã VTCP [/FONT] [FONT=.VnTime] &nbsp; gäi&nbsp; [/FONT] [FONT=.VnTime] +,Gäi lµ mp qua vµ cã VTPT [/FONT] [FONT=.VnTime] +,Gäi lµ mp qua vµ cã VTPT [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; +,§êng vu«ng gãc chung cña vµ lµ giao tuyÕn cña vµ [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] (d) qua giao ®iÓm M cña mp vµ ®êng th¼ngvµ [/FONT]</li>
</ol>[FONT=.VnTime] &nbsp; C¸ch 1:[/FONT] [FONT=.VnTime] +,T×m to¹ ®é giao ®iÓm cña vµ [/FONT] [FONT=.VnTime] +,LËp ph¬ng tr×nh mp qua ®iÓm M vµ [/FONT] [FONT=.VnTime] +,(d) lµ giao tuyÕn cña 2 mp vµ [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; C¸ch 2:[/FONT] [FONT=.VnTime] +,T×m to¹ ®é giao ®iÓm cña vµ [/FONT] [FONT=.VnTime] +,T×m VTCP cña [/FONT] [FONT=.VnTime] &nbsp; &nbsp; T×m VTPT cña [/FONT] [FONT=.VnTime] &nbsp; &nbsp; T×m [/FONT] [FONT=.VnTime] +, (d) lµ ®êng th¼ng qua M vµ cã VTCP&nbsp; [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] vµ c¾t vµ [/FONT]</li>
</ol>[FONT=.VnTime] +, LËp mp chøa vµ [/FONT] [FONT=.VnTime] +,LËp mp chøa vµ [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; +, (d) lµ giao tuyÕn cña vµ [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; +,Chóng tá c¾t vµ [/FONT]<ol>
<li data-xf-list-type="ol">[FONT=.VnTime] Ph¬ng tr×nh h×nh chiÕu (d’) cña (d) lªn mp [/FONT]</li>
</ol>[FONT=.VnTime] +,T×m vµ cã VTCP cña(d)[/FONT] [FONT=.VnTime] +,T×m VTPT cña [/FONT] [FONT=.VnTime] +,T×m [/FONT] [FONT=.VnTime] +,Gäi lµ mp chøa (d) vµ [/FONT] [FONT=.VnTime] qua A vµ co VTPT . ViÕt PTMP [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; +,H×nh chiÕu (d’) cña (d) lªn mp lµ giao tuyÕn cña vµ .PT§T (d’) lµ:[/FONT]&nbsp;&nbsp; [FONT=.VnTime]VÞ trÝ t¬ng ®èi cña ®êng th¼ng vµ mÆt ph¼ng:[/FONT]&nbsp; [FONT=.VnTime] Cho (d) :&nbsp; qua&nbsp; vµ cã VTCP&nbsp; vµ mÆt ph¼ng&nbsp; cã VTPT [/FONT][FONT=.VnTime][/FONT] [FONT=.VnTime] &nbsp; &nbsp; c¾t [/FONT]&nbsp; &nbsp;&nbsp; [FONT=.VnTime] cïng ph¬ng [/FONT]&nbsp; [FONT=.VnTime] &nbsp; &nbsp; víi&nbsp;&nbsp; vµ Kho¶ng&nbsp; c¸ch :[/FONT]&nbsp;&nbsp; [FONT=.VnTime][/FONT]&nbsp; [FONT=.VnTime] Kho¶ng c¸ch tõ&nbsp;&nbsp; mÆt ph¼ng [/FONT]&nbsp;&nbsp; [FONT=.VnTime] &nbsp; Kho¶ng c¸ch tõ&nbsp; ®Õn (d) :&nbsp; qua&nbsp; vµ cã VTCP [/FONT]&nbsp;&nbsp; [FONT=.VnTime] Kho¶ng c¸ch gi÷a 2 ®êng th¼ng chÐo nhau:[/FONT] [FONT=.VnTime] &nbsp;&nbsp; Trong kh«ng gian cho 2 ®êng th¼ng chÐo nhau:[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp;&nbsp; qua vµ cã VTCP [/FONT] [FONT=.VnTime] &nbsp; &nbsp;&nbsp; qua vµ cã VTCP [/FONT]&nbsp; [FONT=.VnTime] Chó ý: cã thÓ tÝnh kho¶ng c¸ch gi÷a vµ&nbsp; b»ng c¸ch lËp ph¬ng tr×nh mÆt ph¼ng chøa vµ //&nbsp; . TÝnh kho¶ng c¸ch tõ MÆt cÇu:[/FONT]&nbsp; &nbsp;&nbsp; [FONT=.VnTime][/FONT]&nbsp; [FONT=.VnTime] Ph¬ng tr×nh mÆt cÇu (S) t©m I(a,b,c) b¸n kÝnh R:&nbsp;&nbsp; [/FONT]&nbsp; [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; Hay:&nbsp; [/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; ®iÒu kiÖn: [/FONT]&nbsp;&nbsp; [FONT=.VnTime] Ph¬ng tr×nh ®êng trßn:&nbsp; [/FONT]&nbsp; [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp; B¸n kÝnh&nbsp; &nbsp; [/FONT]&nbsp; [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Víi&nbsp; &nbsp; R: b¸n kÝnh mÆt cÇu (S)[/FONT] [FONT=.VnTime] &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; d: kho¶ng c¸ch tõ t©m I&nbsp; [/FONT]&nbsp; [FONT=.VnTime] §iÒu kiÖn tiÕp xóc cña mÆt ph¼ng&nbsp; vµ mÆt cÇu (S) lµ: [/FONT]&nbsp;&nbsp; [FONT=.VnTime] Chó ý: Trong ®Ò thi cã nhiÒu bµi lµ h×nh häc kh«ng gian, nhng b»ng sù khÐo lÐo c¸ch chän hÖ trôc to¹ ®é Oxyz ta sÏ ®a bµi to¸n vÒ h×nh häc gi¶i tÝch.[/FONT][FONT=.VnTime] Mét vµi VD vÒ c¸ch chän hÖ trôc to¹ ®é:[/FONT]&nbsp; [FONT=.VnTime] VD1: Cho h×nh chãp tam gi¸c ®Òu S.ABC ®Ønh S, cã ®é dµi c¹nh ®¸y b»ng a.[/FONT]&nbsp;&nbsp; [FONT=.VnTime]&nbsp; Gäi K lµ trung ®iÓm BC. Nªn ta chän hÖ trôc §Òc¸c vu«ng gãc Oyxz sao cho:[/FONT] [FONT=.VnTime] Víi&nbsp; h lµ ®é dµi ®êng cao SH cña h×nh chãp S.ABC VD2: Cho h×nh lËp ph¬ng ABCD.A’B’C’D’ cã c¹nh b»ng a.[/FONT]&nbsp;&nbsp; [FONT=.VnTime]&nbsp; Chän hÖ to¹ ®é §Òc¸c vu«ng gãc Oyxz sao cho:[/FONT]&nbsp; [FONT=.VnTime] VD3: [/FONT]</blockquote>

[QUOTE="i love all, post: 71892, member: 74430"] [FONT=.VnTime][B] Phư¬ng ph¸p gi¶i h×nh häc gi¶i tÝch trong kh«ng gian [/B] [/FONT] [FONT=.VnTime] [SIZE=4]H×nh häc gi¶i tÝch trong kh«ng gian lu«n cã trong c¸c ®Ò thi vµo ®¹i häc, tèt nghiÖp trung häc phæ th«ng, bµi viÕt nµy lµ tæng hîp c¸c d¹ng cña ®Ò thi. Mong bµi viÕt nµy cã thÓ gióp cho c¸c b¹n cã thÓ häc tèt vµ lµm bµi h×nh häc gi¶i tÝch ®îc tèt h¬n trong c¸c k× thi.[/SIZE] [B]A,Lý thuyÕt:[/B][/FONT] [FONT=.VnTime] [B] [SIZE=4]Quy t¾c h×nh hép[/SIZE][/B][/FONT] [FONT=.VnTime] [SIZE=4]: ABCDA’B’C’D’ lµ h×nh hép th× : [/SIZE] [B] [SIZE=4]3 vect¬ ®ång ph¼ng: [/SIZE][/B][/FONT] [FONT=.VnTime] [SIZE=4]®ång ph¼ng khi :[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] HoÆc sao cho [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] HoÆc [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4][B]TÝch v« híng cña 2 vect¬: [/B]cho [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Ta cã : [/SIZE] [/FONT] [FONT=.VnTime][B] [SIZE=4]TÝnh chÊt: [/SIZE][/B] [/FONT] [FONT=.VnTime] [SIZE=4]+, cïng ph¬ng [/SIZE][/FONT][FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4] +, vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] [B]HÖ qu¶:[/B][/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4][B] +, [/B][/SIZE][/FONT][FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4][B] +, [/B](diÖn tÝch h×nh b×nh hµnh)[/SIZE][/FONT][FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4][B] +, [/B](thÓ tÝch h×nh hép)[/SIZE][/FONT][FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4] +, (thÓ tÝch tø diÖn)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, ®ång ph¼ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] kh«ng ®ång ph¼ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, Gãc cña 2 mÆt ph¼ng : lµ: [/SIZE] [B]B, Ph¬ng ph¸p gi¶i:[/B][/FONT] [FONT=.VnTime] I,MÆt ph¼ng: [/FONT] [FONT=.VnTime] [SIZE=4] PTTQ(ph¬ng tr×nh tæng qu¸t) mÆt ph¼ng(mp) qua vµ cã VTPT(vect¬ ph¸p tuyÕn) lµ: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] hay : víi [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] PTMP(ph¬ng tr×nh mÆt ph¼ng) qua cã ph¬ng tr×nh(pt) lµ: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] KÕt qu¶:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,PTMT to¹ ®é oxy: z=0[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,PTMT to¹ ®é oxz: y=0[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,PTMT to¹ ®é oyz: x=0[/SIZE] [/FONT] [FONT=.VnTime]VÞ trÝ t¬ng ®èi cña mÆt th¼ng vµ mÆt ph¼ng: [/FONT] [FONT=.VnTime] [SIZE=4]Cho [/SIZE] [B]Ph¬ng tr×nh chïm mÆt ph¼ng:[/B][/FONT] [FONT=.VnTime] [SIZE=4]TËp hîp c¸c mÆt ph¼ng chøa ®êng th¼ng ®îc gäi lµ chïm mÆt ph¼ng x¸c ®Þnh bëi mp vµ mp . NÕu vµ th× ph¬ng tr×nh mÆt ph¼ng lµ:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] (*) víi [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]ph¬ng tr×nh (*) cã thÓ viÕt l¹i: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] C¸c vÊn ®Ò: ViÕt PTMP(ph¬ng tr×nh mÆt ph¼ng):[/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP qua vµ cã VTPT [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,X¸c ®Þnh cña mp[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,X¸c ®Þnh VTPT [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,¸p dông c«ng thøc : [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP qua vµ cã cÆp VTCP(vect¬ chØ ph¬ng) [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4](víi cã gi¸ song song hoÆc n»m trªn mp ) [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m VTPT [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, lµ mp qua vµ cã VTPT [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP qua 3 ®iÓm kh«ng th¼ng hµng A,B,C[/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m VTPT [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, lµ mp qua A vµ cã VTPT [/SIZE] [/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP qua vµ vu«ng gãc víi 2 mp vµ c¾t nhau[/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4] +,T×m VTPT cña vµ lµ vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,T×m VTPT cña [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, lµ mp qua vµ cã VTPT [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime] [SIZE=4][B]PTMP qua vµ qua giao tuyÕn 2mp c¾t nhau[/B] [B]lµ vµ [/B][/SIZE][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+, cã d¹ng : (*) víi [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, qua thÕ vµo ph¬ng tr×nh (*)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,Rót ra m theo n chän m,n råi thÕ vµo phong tr×nh (*)[/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP qua vµ vu«ng gãc víi ®êng th¼ng (d)[/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m VTCP cña (d)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, lµ mp qua vµ cã VTPT = [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP qua vµ chøa ®êng th¼ng (d)[/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4] TH1: (d) cã d¹ng tæng qu¸t[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, T×m PTMP ta dïng c«ng thøc chïm mp.[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] TH2: (d) cã d¹ng chÝnh t¾c[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] C¸ch 1: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, ChuyÓn ph¬ng tr×nh (d) vÒ d¹ng ph¬ng tr×nh t«ng qu¸t[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,Dïng c«ng thøc chïm mp[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] C¸ch 2: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,T×m vµ cã VTCP cña (d)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,T×m [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, lµ mp qua vµ cã VTPT [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PTMP chøa ®êng th¼ng vµ // [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m vµ cã VTCP cña [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m VTCP cña [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, lµ mp qua A vµ cã VTPT [/SIZE] [/FONT] [FONT=.VnTime]II,§êng th¼ng: [/FONT] [FONT=.VnTime] [SIZE=4] PTTQ(ph¬ng tr×nh tæng qu¸t): [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]VTCP(vect¬ chØ ph¬ng): [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]§Æc biÖt:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,ph¬ng tr×nh trôc ox: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,ph¬ng tr×nh trôc oy: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,ph¬ng tr×nh trôc oz: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]PTTS(ph¬ng tr×nh tham sè): (d) qua vµ cã VTCP :[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] (d) : [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]PTCT(ph¬ng tr×nh chÝnh t¾c): (d) : [/SIZE] [/FONT] [FONT=.VnTime]VÞ trÝ t¬ng ®èi cña ®êng th¼ng vµ ®êng ph¼ng: [/FONT] [FONT=.VnTime] [SIZE=4]Cho qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] chÐo nhau kh«ng ®ång ph¼ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] ®ång ph¼ng ®ång ph¼ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] ®ång ph¼ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] c¾t nhau [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] kh«ng cïng ph¬ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] cïng ph¬ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] song song [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] cïng ph¬ng[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] trïng nhau [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Cã víi [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]C¸c vÊn ®Ò: ViÕt PT§T(ph¬ng tr×nh ®êng th¼ng)[/SIZE] [B]TH1:§êng th¼ng (d) ®îc x¸c ®Þnh bëi 1 ®iÓm vµ 1 VTCP[/B][/FONT] [FONT=.VnTime] [B] [SIZE=4]1.[/SIZE] [/B][/FONT] [FONT=.VnTime][B] [SIZE=4]PT§T (d) qua vµ cã VTCP [/SIZE][/B] [/FONT] [FONT=.VnTime] [SIZE=4]+,Dïng PTTS hay PTCT[/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua vµ (d) song sonh víi 1 ®êng th¼ng cho tríc[/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m VTCP cña (d)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ ®êng th¼ng quavµ cã VTCP [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua vµ (d) song sonh víi 2 mp c¾t nhau [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m VTPT cña mp : [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] T×m VTPT cña mp : [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ ®êng th¼ng quavµ cã VTCP [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua vµ [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+T×m VTPT cña mp lµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ ®êng th¼ng quavµ cã VTCP = [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua vµ (d) vu«ng gãc víi 2 ®êng th¼ng vµ [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m VTCP cñalµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,T×m VTCP cñalµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Gäi [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,(d) lµ ®êng th¼ng quavµ cã VTCP [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua , vµ (d) c¾t [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,LËp PTMP qua vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m giao ®iÓm N cña vµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ ®êng th¼ng ®i qua 2 ®iÓm vµ N [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua vµ (d) c¾t 2 ®êng th¼ng , cho tríc[/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4] C¸ch 1:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, LËp PTMP qua vµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m giao ®iÓm N cña vµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ ®êng th¼ng qua ,N[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,Chøng tá (d) c¾t [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] C¸ch 2:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, LËp PTMP qua vµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, LËp PTMP qua vµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ giao tuyÕn cña vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,Chøng tá (d) c¾t [B], [/B][/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime][B] [SIZE=4]PT§T (d) qua , vµ (d) c¾t [/SIZE][/B][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,LËp PTMP qua vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m giao ®iÓm N cña vµ[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, (d) lµ ®êng th¼ng qua M,N[/SIZE] [B]TH2: (d) x¸c ®Þnh lµ giao tuyÕn cña 2 mÆt ph¼ng:[/B][/FONT] [LIST=1] [*][FONT=.VnTime] [SIZE=4]Ph¬ng tr×nh ®êng vu«ng gãc chung cña 2 ®êng th¼ng chÐo nhau vµ [/SIZE][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,Trong kh«ng gian cho 2 ®êng th¼ng chÐo nhau:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] gäi [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,Gäi lµ mp qua vµ cã VTPT [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,Gäi lµ mp qua vµ cã VTPT [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,§êng vu«ng gãc chung cña vµ lµ giao tuyÕn cña vµ [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime] [SIZE=4](d) qua giao ®iÓm M cña mp vµ ®êng th¼ngvµ [/SIZE][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4] C¸ch 1:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m to¹ ®é giao ®iÓm cña vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,LËp ph¬ng tr×nh mp qua ®iÓm M vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,(d) lµ giao tuyÕn cña 2 mp vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] C¸ch 2:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m to¹ ®é giao ®iÓm cña vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m VTCP cña [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] T×m VTPT cña [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] T×m [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+, (d) lµ ®êng th¼ng qua M vµ cã VTCP [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime] [SIZE=4]vµ c¾t vµ [/SIZE][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+, LËp mp chøa vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,LËp mp chøa vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +, (d) lµ giao tuyÕn cña vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,Chóng tá c¾t vµ [/SIZE][/FONT] [LIST=1] [*][FONT=.VnTime] [SIZE=4]Ph¬ng tr×nh h×nh chiÕu (d’) cña (d) lªn mp [/SIZE][/FONT] [/LIST] [FONT=.VnTime] [SIZE=4]+,T×m vµ cã VTCP cña(d)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m VTPT cña [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,T×m [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]+,Gäi lµ mp chøa (d) vµ [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]qua A vµ co VTPT . ViÕt PTMP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] +,H×nh chiÕu (d’) cña (d) lªn mp lµ giao tuyÕn cña vµ .PT§T (d’) lµ:[/SIZE] [/FONT] [FONT=.VnTime]VÞ trÝ t¬ng ®èi cña ®êng th¼ng vµ mÆt ph¼ng: [/FONT] [FONT=.VnTime] [SIZE=4][B]Cho [/B](d) : qua vµ cã VTCP vµ mÆt ph¼ng cã VTPT [/SIZE][/FONT][FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4] c¾t [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] cïng ph¬ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] víi vµ [/SIZE] [B]Kho¶ng c¸ch :[/B][/FONT] [FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4] Kho¶ng c¸ch tõ mÆt ph¼ng [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Kho¶ng c¸ch tõ ®Õn (d) : qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]Kho¶ng c¸ch gi÷a 2 ®êng th¼ng chÐo nhau:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Trong kh«ng gian cho 2 ®êng th¼ng chÐo nhau:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] qua vµ cã VTCP [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] [B]Chó ý:[/B] cã thÓ tÝnh kho¶ng c¸ch gi÷a vµ b»ng c¸ch lËp ph¬ng tr×nh mÆt ph¼ng chøa vµ // . TÝnh kho¶ng c¸ch tõ [/SIZE] [B]MÆt cÇu:[/B][/FONT] [FONT=.VnTime] [/FONT] [FONT=.VnTime] [SIZE=4]Ph¬ng tr×nh mÆt cÇu (S) t©m I(a,b,c) b¸n kÝnh R: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Hay: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] ®iÒu kiÖn: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Ph¬ng tr×nh ®êng trßn: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] B¸n kÝnh [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Víi R: b¸n kÝnh mÆt cÇu (S)[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] d: kho¶ng c¸ch tõ t©m I [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]§iÒu kiÖn tiÕp xóc cña mÆt ph¼ng vµ mÆt cÇu (S) lµ: [/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4][B]Chó ý: [/B]Trong ®Ò thi cã nhiÒu bµi lµ h×nh häc kh«ng gian, nhng b»ng sù khÐo lÐo c¸ch chän hÖ trôc to¹ ®é Oxyz ta sÏ ®a bµi to¸n vÒ h×nh häc gi¶i tÝch.[/SIZE][/FONT][FONT=.VnTime] [B] [SIZE=4]Mét vµi VD vÒ c¸ch chän hÖ trôc to¹ ®é:[/SIZE][/B][/FONT] [FONT=.VnTime] [B] [SIZE=4]VD1: Cho h×nh chãp tam gi¸c ®Òu S.ABC ®Ønh S, cã ®é dµi c¹nh ®¸y b»ng a.[/SIZE][/B][/FONT] [FONT=.VnTime] [SIZE=4] Gäi K lµ trung ®iÓm BC. Nªn ta chän hÖ trôc §Òc¸c vu«ng gãc Oyxz sao cho:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4] Víi h lµ ®é dµi ®êng cao SH cña h×nh chãp S.ABC[/SIZE] [B] [SIZE=4]VD2: Cho h×nh lËp ph¬ng ABCD.A’B’C’D’ cã c¹nh b»ng a.[/SIZE][/B][/FONT] [FONT=.VnTime] [SIZE=4] Chän hÖ to¹ ®é §Òc¸c vu«ng gãc Oyxz sao cho:[/SIZE] [/FONT] [FONT=.VnTime] [SIZE=4]VD3: [/SIZE][/FONT] [/QUOTE]

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