已知向量m=(1,0),n=(1/2,-√3/2）,且a=m+2n,b=2m-3n,求a与b的夹角

题目

已知向量m=(1,0),n=(1/2,-√3/2）,且a=m+2n,b=2m-3n,求a与b的夹角
答案=120°

答案

a=m+2n=(2,-√3)
b=2m-3n=(1/2,3√3/2)
cos=a*b/|a||b|=(1-9/2)/(√7)^2=-1/2
a与b的夹角=120°