1、 1 2017 8.2 45 a b c ( ) A c c B b b C b c a b c a b D b c c b c B A c c c B b b C b c a a b b c b c D b c b c c c . B. 2 m n ( ) A m n m n B m n m n C m n m n D m n m n D A m n A B m n B C m n C D D 3 a l a a a b c b c ( ) A B C D D b c D. 4 a b c a M b N M N c. a b c a b a c a b a b a c a b a c M
2、N. ( ) A 0 B 1 C 2 D 3 C a b b c M N C. 2 ABCD A1B1C1D1 AA1 2AB E AA1 D1C BE ( ) A. 1 5B. 3 10 10C. 10 10D. 3 5 B A1B. A1D1 BC A1D1CB D1C A1B. A1BE D1C BE AA1 2AB 2 A1E 1 BE 2 A1B 5 A1BE cos A1BE A1B 2 EB 2 A1E 2 2A1B EB 5 2 1 5 2 3 10 10 B. a b c a b b c a c a b b c a c a b b c a c a b a b _( ) 4 a
3、 b b c a c a b b c a c a b a b 7 ABC A1B1C1 ACB AA1 2 AC BC 1 A1B AC _ 3 6 6 AC A1C1 BA1C1( ) BA1C1 A1B 6 A1C1 1 BC1 5 cos BA1C1 6 1 5 2 6 6 6 . 8 ABCD E F AC BD CD 2AB 2 EF AB EF CD _ H DA HF HE FH EF. Rt EFH HE 1 HF 1 2 HEF EF CD 9 ABCD E F AB AD EF AF BE _ 4 1 2 F HF BE A EF AG G. HG HE AH. ABCD
4、2 AEF BCDFE AG EF AG BCDFE. BE BH AE AF 1 EH EF 2. G EF EG 2 2 AG 2 2 . HF 2 HEG Rt EHG HG 2 2 2 2 2 10 2 . Rt AGH AH 10 2 2 2 2 2 3. HF BE AF BE AFH. AHF AF 1 HF 2 AH 3 HAF cos AFH AF HF 1 2 . 10 ABCD A1B1C1D1 M N CD CC1 A1M DN _ 5 D1M D1M A1M DCC1D1 DCC1D1 M N CD CC1 D1M DN A1M DN. A1M DN 11 S ACB
5、 SAB SAC ACB AC 2 BC 13 SB 29 SC AB _ 17 17 BC E ABC DE AB SBC EF SC SC AB FED F FG AB DG DFG AC 2 BC 13 SB 29 DE 17 2 EF 2 DF 5 2 DEF cos DEF DE 2 EF 2 DF 2 2DE EF 17 17 . 6 A AB AS y z y z x AC 2 BC 13 SB 29 B(0 17 0) S(0,0 2 3) C 2 13 17 4 17 0 SC 2 13 17 4 17 2 3 AB (0 17 0) SC AB SC AB 4 |SC |A
6、B | 4 17 cos |SC AB | |SC |AB | 17 17 . 12 P ABCD 2 DAB AC BD O PO ABCD PB ABCD (1) (2) E PB DE PA (1) P ABCD PO ABCD PBO PB ABCD PBO Rt AOB AB 2 BO AB 1. Rt POB PO OB PO BO 3 S 1 2 3 2 2 3 P ABCD VP ABCD 1 3 3 3 2. 7 (2) AB F EF DF. E PB EF PA DEF DE PA ( ) Rt AOB AO AB 3 OP Rt POA PA 6 EF 6 2 . AB
7、D PDB DF DE 3 cos DEF DE 2 EF 2 DF 2 2DE EF 3 2 6 2 2 3 2 3 6 2 6 4 3 2 2 4 . DE PA 2 4 . m n m n l l( ) A m n B m n C m n D m n B l m n l m l n. m n C D A m n l m n l 14 ABC A1B1C1 BAC AB AC AA1 BA1 AC1 ( ) A C 8 C AB AA1 A1C1 D E F BA1 DE AC1 EF. BA1 AC1 DEF( ) AB AC AA1 2 DE EF 2 DF 6 cos DEF DE
8、2 EF 2 DF 2 2DE EF 1 2 DEF BA1 AC1 15 D ABC O DO AB ( ) A. 3 3B. 1 2C. 3 D. 2 2 A 9 A AB AC AD AB AC 2 AD 1 O BC AC E DE DO OE OE 1 AE 1 OE AB DOE Rt DAE DE 2 O Rt ABC AO 2 DAO DO 3. DOE cos DOE 1 3 2 3 3 3 3 3 . 16 P ABC PA ABC BAC PA AB AC 2 E PC (1) AE PB AE PB (2) A EBC (1) AE PB A B E ABE P ABE P ABE 10 AE PB BC F EF AF EF PB AEF AE PB BAC PA AB AC 2 PA ABC AF 3 AE 2 EF 2 cos AEF 2 2 3 2 2 1 4 AE PB 1 4 . (2) E PC E ABC 1 2 PA 1 VA EBC VE ABC 1 3 1 2 3 2 3 3 .
