1,已知向量a=(2,-1),b=(x,x^2-1),且 a与b的夹角为锐角
则a·b＜0
(2,-1)·(x,x^2-1)＜0
即2x-x^2+1＜0
x^2-2x-1＞0
解得x＞1+√2或x＜1-√2
2,由|a|=4,|b|=3得a^2=16,b^2=9,
由(2a-3b)(2a+b)=61得
4a^2-4a·b-3b^2=61
即4*16-4a·b-3*9=61
a·b=-6
cosθ=（a·b）/(|a|*|b|)=-6/(4*3)=-1/2
θ=120°
即a与b的夹角为120°
3,a=(2,2),b=(1/2,-1/2),c=(-1,2),
设c=xa+yb
即(-1,2)=x(2,2)+y(1/2,-1/2)
=（2x,2x)+(y/2,-y/2)
=(2x+y/2,2x-y/2)
所以2x+y/2=-1,且2x-y/2=2
解得x=0.5,y=-4
所以c=0.5a-4