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?
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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?
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?
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?
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 λ
cos= ----------------------- = ------------- =cos120°
|OA+λOB||OB| √2λ+1²
解得:λ=±1/2