1、 1 ( 4) 1 1,10 4,6,9 2,8 3,11 5,7,12,13,14 ( :30 ) 1. : , ; + =0; , ; , A B C D . ( A ) (A)2 (B)3 (C)4 (D)1 : ; + =0, 0; ; , . A. 2. , a= b , a b ( A ) (A) (B) (C) (D) : a 0,b=0,a= b . 3. =a+2b, =-5a+6b, =7a-2b, ( B ) (A)A,B,C (B)A,B,D (C)B,C,D (D)A,C,D : = + =-5a+6b+7a-2b=2a+4b=2 , A,B,D . 2 4.(201
2、6 ) M ABC AB , = , ( D ) (A) + (B)2 -2 (C) + (D) + : , = , = , = + = + = +( - ) = + . 5. , ABC , = ,P BN , =m + , m ( C ) (A)3 (B)1 (C) (D) : = ( R), = + = + 3 = + ( - ) = + ( - ) =(1- ) + , m=, C. =m + =m + , B,P,N , m+=1, m=. C. 6.(2016 ) ABC ,AB=2,BC=3, ABC=60 ,AD BC ,O AD , = + , + ( D ) (A)1 (B
3、) (C) (D) : Rt ABD ,BD=AB cos60 =1, =, = . = + = + , 2 = + , = + , =, =, + =+=. D. 7.(2015 ) ABC ,AB=3,AC=2, = + , AD ABC ( C ) (A) (B) (C) (D) 4 : AB=3,AC=2, | |=,| |=. | |=| |=, = , = , | |=| |, = + = + . , AEDF , AD , AD EAF, AD ABC . 8.(2015 ) e1,e2 , a=e1+ke2,b=ke1+e2, a b k . :a b a= b, e1+ke2
4、= (ke1+e2)= ke1+ e2, e1,e2 , k= 1. : 1 9. D,E,F ABC BC,CA,AB , =a, =b, : =a-b; =a+b; =-a+b; + + =0. . : =a, =b, = + =-a-b, 5 = + =a+b, =( + )=(-a+b)=-a+b, + + =-b-a+a+b+b-a=0. . : 10. : ; a b , a b ; , ; . . : , , ; 0 , ; , , ; , . : ( :15 ) 11.(2015 ) i j , =i+mj, =n i+j. A,B,D , m,n ( C ) (A)m+n=1
5、 (B)m+n=-1 (C)mn=1 (D)mn=-1 : A,B,D = ( R), i+mj= (ni+j)= ni+ j, i,j , mn=1. 12. ABC ,P BC , A,B,C a,b,c, c +a +b =0, ABC ( C ) (A) 6 (B) (C) (D) : c -a( + )+b( - )=0, (c- ) - =0, (c- ) = , , , a=b=c. 13.(2016 ) O ABC , +2 +3 =0, AOB, AOC, BOC . : , OB E, =2 , , OAFE, +2 = + = , +2 +3 =0, - =3 , = =
6、2 , 7 =2 , = , S ABC=2S AOB; S ABC=3S AOC,S ABC=6S BOC, AOB, AOC, BOC =3 2 1, :3 2 1 14.(2015 ) , OCB ,B,C A ,D OB 2 1 ,DC OA E, =a, =b. (1) a,b , ; (2) = , . :(1) A BC , = , + =2 , =2 - =2a-b, = - =2a-b-b=2a-b. (2) , = - =2a-b- a=(2- )a-b, =2a-b, 8 =, =. 5 (2015 ) ABC , M,N AB,AC , =2 , = , CM BN P
7、, =a, =b, a b ( A ) (A) =a+b (B) =a+b (C) =a+b (D) =a+b : . : =a, =, =b, = b, = - =b-a, = - =b-a. = = (b-a), = = (b-a), - = , (b-a)- (b-a)=a, = + =a+(b-a)=a+b. (2015 ) A,B,C l ,O l , 9 p +q +r =0. p,q,r R, p+q+r= . : . : A,B,C l , ( 0) = . - = ( - ), ( -1) + - =0. p +q +r =0, r=0 , p=q=0, p+q+r=0; r 0 , p,q 0, =. p+q+r=0. :0
