31 BÀI TOÁN HHKG LỚP 11 ÔN THI HK 2

31 BÀI TOÁN ÔN TẬP HÌNH HỌC KHÔNG GIAN- HỌC KỲ II - LỚP 11  !"#$%&'(%)*+ Bài 1,- --/012,3/456 -7,389:;< 1 =,3>⊥ 2?<<@5A 5BC856 --D7/EF4G:8H-1<1,<6132 FI,I: , =1>< ,3 =13>< 3 =1,>⊥ ⊥ ⊥ JI,I: 1, =@>⊥ 6  =@>∈ 2 I,I: @ =1,>⊥ 8K4/HF @ ⊥ 2 Bài2,- --/012,3/456 -8-,389:;6/ 1 1,<1 13= = 2 FI,I: 1; =,3>⊥ 2 JI?<@5A5BC8568H4G:EF-<,2,I:H @ =13>⊥ 6 @ 13⊥ 2 Bài 3,-8LM;,/'- ;<;<;, 47:N87/O-F2@P ; =,>⊥ 82 ,I: FI ; ,<; ,⊥ ⊥ 6 ;,  ⊥ 2 JI568HQ89:EF ,V 2 I ) ) ) ) * * * * ; ; ; ;, = + + Bài4,-8LM,3/  =,3>⊥ 2H ,3V R4BSF"63TU8-F8;2 H:0=,3>R 3@ , ⊥ 8@2?568HQ89:EF ,3V 2 FI,I: :0=3,> :0=">⊥ <6 :0=3,> :0=3T@>⊥ 2 JI,I: ; :0=3,>⊥ 2 Bài5F8F:9,63,V:8H):W80-XY--F/--4,8 8LM,32?568H4G:-,2 FI,I: , 3⊥ 2 JI?564BSFEF 3V 2,I:H  =,3>⊥ 2 Bài 6*,- --/012,3/456 -8-,389:</-JVF64BS-Z 3[F2,- F \ 1, ) = 7/O:0=,3>2,I: :0=1> :0=13>⊥ 2 Bài 7/8,- --/012,3/456 -8-,3-F6/ 1 1 1, F= = = 2,I: FI:0 =,3> :0=13>⊥ JI 13V 7812 Bài8/ 9,-8LM1,/ 1 =,>⊥ 2?6@5A5BC8568HQ89:EFEF ,V 6 1,V 2,I:H FI <1@<, 4]^2 JI 1, =@>⊥ 6 =1,> =@>⊥  I @ =1,>⊥ 6 =1,> =@>⊥ Bài 9/10,-8LM1,/'4_-<<,88-6-:N88F:794_-6 , )F = ` 1 =,>⊥ 6 1 F = 2 FI,I: :0=1> :0=1,>⊥ JIH:0=1>R  1 ⊥ 82,I:  =1,>⊥ 2 Ia-4NL642 LIK8H4G:;EF4,R ;@ =1,>⊥ U8=1,>8@2a-4NL64;@2 Bài 10/12,- --/012,3/456 -8-F,37863`JD8  )F<3 3, F` 1 =,3><1 F= = = ⊥ = 2 FI,I: =13> =13,>⊥ 6 =1,> =1,>⊥ 2 JI? ϕ 56/bF):W80-X=1,>6=,3>2a- 8F ϕ 2 I? = >α 56:W80-X-F1367/O:0=1,>2cd4e- = >α 6d4e-8-D8LM EF --/012,3O = >α 2a-LM8a-8-D8LM4/2 Bài 11/13,- --/012,3/456 -7,389:;< 1 =,3>⊥ 61[F2? <f5A5BC8568H4G:EF1,62 FI,I: ; =,3>⊥ 2 JIa- L=`,f> 2 Bài 12/14,- ,V O[(<,[&<,[%2H4BS8-X7/O:0=,>8 5g4G:;F-;[+2a- L=;`,> 2 Bài 13/15*,- ,V 78</-[FV:8H:0 = >α < , F )= 68O = >α :N8 / # \# 2 FIa- [ ] L ,`= > ,α = JI,I:H,-,8O = >α :N8/ # +&ϕ = 2 Bài 14/16*, 1 =,3>⊥ 61[-23Q68a-4NL647/-EF FI16,3JI1,63 Bài 15/18,- --/012,3/456 -7,389:;<[F2BSF1;EF --/07/O:W84=,3>6/1;[F2a-Y-h-bF)4BS8-X-Z -F1,62 Bài 16/ 20,- --/08F:4i12,/-4JV'F<-JJV)F2?568H? 89:EF ,V 2 FIa- [ ] L 1`=,> JIa- L=`1> 2 Bài 17/21*,- --/08F:12,/4568F:4i-(F` 1, =,>⊥ 61,[(F2 FIa-/bF16,2JIa- L=1`,> Bài 18/22,- -8-,389:;<-F6/ F ' ; ' = 2H4BS8-X7/O :0=,3>8;8F5g:N84G:1F-1[F2 FI,I: 1,V 568F:76 1, 3⊥ JI,I: =13> =1> `=1,> =1,3>⊥ ⊥ 2 Ia- L=1`3> 2 LIa-/bF= α >6=,3>2 Bài 19/28 :,-8LM;,/ ; ; ;, F = = = 6 · · · # # ; ;, \# `;, $#= = = 2 FI,I8j ,V 56:N88F:72 JI,I: ; , ⊥ 2?<k5A5BC8568H4G:EF;6,2,-8jk564BS7/- EF;6,2 Bài 20/29H:0 = >α -4BS8Hl4BSYa-2g:N84G: 1 = >∉ α F- 1 = >⊥ α 2? 56:N84G:8H4BS8HlY-O62 FI,I:H:0=1> ⊥ :0=1>2 JIH:0=1>R @ 1 ⊥ 8@2,I: @ 1 ⊥ 2 Bài 21/ 31,- --/012,3/456 -J.--6-O[F<3[)F2 1V 79 82f564G:8H-3=fY-63>2fW80-X α ^FfO:0=1>U8,< 1,<135A5BC88<<!2 FI,I:f!56 -8-F72 JIW8d[f2a-LM8a-EFf!8-mF6d2 Bài 22/32,-8LM4i,3-JVF`?f568H4G:EF,2a-EF/ · =<3f> 2 Bài 23/33,-8LM,3/):W8,63,56)8F:9/-4,2 FI,I:H , 3 ⊥ JI?568H4G:EF,<564BSFEF 3V 2,I:  =,3>⊥ 2 Bài 24/34,- --/012,3/456 -8-,389:;2D81[1,<1[132,I:H FI 1; :0=,3>⊥ JI , 13⊥ Bài 25/35,- --/012,3/4,356 --b-n8<[F< 3 F '= 2,-J1 7/O461[F2a- FI/bF · =1`,3> JI/bF · =13`=1>> I/bF · ==1,3>`=,3>> Bài 26/37,- --/012,3/456 -7,3-F2 1 :0=,3>⊥ <1[F2o 4e-68a-4NL647/EFW04BS8-X FI163JI1,63I16,3 Bài 27/38,- --/012,3/456 -7,3-F6 1 1 1, 13 F )= = = = 2 ?6k5A5BC8568H4G:EF36,2 FI,I: :0=1k> :0=1,>⊥ JIa- L=3`1> Bài 28/39,-5p8Hq,2rr,r/8g8h-44iJVF2D8/88-6-Js- J6:W8456 # \# 6 --DEF4_-5:W80-X=rr,r>8HtO8H4G:EF -r,r2 FIa-Y-h-bF):W84JIa-8F=,<,r>2 Ia-8FEF/bF:0=rr>6:W842 Bài 29/40,-8LM,3/,568F:4i-F< 3 , ⊥ <3[F6Y-h-8K3 4D,56F2?568H4G:EF,6568H4G:EF2 FI,I: , :0=3>⊥ 63[F2JI,I: 3 =,>⊥ Io4e-68a-4NL647/-EF)4BS8-X36,2 Bài 30/41,- --/012,3/456 -8-,389:;<-F2/ µ #  \#= 6/4BS F1;[F2 FIa- [ ] L ;`=1,> JIa- L=3`1> Bài 31/45*:,-8LM1,/ · # , $#= <[)F< , F '= 2 1 =,>⊥ <1[)F2?f56 8H4G:EF2 FIa-/bF):W80-X=1,>6=,>2 JIa-4BSF@EF f,V 2 Ia- 8F ϕ O · ==1f,>`=,>>ϕ = 2 LIa- [ ] L `=1f,> 2  Chúc các em thành công! . 31 BÀI TOÁN ÔN TẬP HÌNH HỌC KHÔNG GIAN- HỌC KỲ II - LỚP 11  !"#$%&'(%)*+ Bài 1,- --/0 12 ,3/456. -J.--6-O[F<3[)F2 1V 79 8 2 f564G:8H-3=fY-63>2fW80-X α ^FfO:0=1>U8,< 1,<135A5BC88<<! 2 FI,I:f!56 -8-F7 2 JIW8d[f2a-LM8a-EFf!8-mF6d2 Bài 22 / 32 ,-8LM4i,3-JVF`?f568H4G:EF ,2 a-EF/ · =<3f> 2 Bài. `;, $#= = = 2 FI,I8j ,V 56:N88F:7 2 JI,I: ; , ⊥ 2 ?<k5A5BC8568H4G:EF;6, 2, -8jk564BS7/- EF;6 ,2 Bài 20 /29 H:0 =