设向量a,b满足a+2b=(2,-4),3a-b=(-8,16),求a·b

问题描述:

设向量a,b满足a+2b=(2,-4),3a-b=(-8,16),求a·b

a+2b=(2,-4),①
3a-b=(-8,16)②
①+2×②,得
7a=(2-8×2,-4+16×2)=(-14,-28)
a=(-2,-4)
2b=(2,-4)-a=(2,-4)-(-2,-4)=(4,0)
b=(2,0)
所以
a·b=(-2,-4)·(2,0)=-2×2+(-4)×0=-4