Question

已知单位向量a,b,c满足a+b+c=0,求a与b的夹角? 如题

Answer 1

单位向量a,b,c
则|a|=|b|=|c|=1
设向量a与b的夹角是θ
a+b=-c
(a+b)^2=c^2
a^2+b^2+2ab=c^2
|a|^2+|b|^2+2ab=|c|^2
1+1+2cosθ=1
cosθ=-1/2
θ=2π/3=120°