若e1,e2是夹角为60°的两个单位向量,求a=2e1+e2,b=-3e1+2e2的夹角

2025-01-24 20:53:17
推荐回答(1个)
回答1:

a*b=(2e1+e2)(-3e1+2e2)
=-6+e1e2+2
=-4+e1*e2
=-4+cos60°
=-4+1/2
=-7/2
|a|²=|2e1+e2|²=5+4e1e2=5+2=7
|b|²=|-3e1+2e2|²=13-12e1e2=13-6=7

cos夹角=a*b/|a||b|=(-7/2)/7=-1/2
所以
夹角=120°