Question

已知A(1,0,0),B(0,-1,1),向量OA+向量λOB 与向量OB的夹角为120°,则λ的值为多少?

Answer 1

O点是原点吧OA=(1,0,0)OB=(0,-1,1)OA+λOB=(1,0,0)+λ(0,-1,1)=(1,-λ,λ)(OA+λOB)OB λcos= ----------------------- = ------------- =cos120° |OA+λOB||OB| √2λ+1²解得:λ=±1/2