已知a,b,c为单位向量,且满足3a+λb+7c=0,a与b的夹角为π/3,这实数λ=
问题描述:
已知a,b,c为单位向量,且满足3a+λb+7c=0,a与b的夹角为π/3,这实数λ=
答
3a+λb+7c=0
故3a+λb=-7c,两边取模|3a+λb|=|-7c|=7
两边平方9a^2+6λa*b+λ^2b^2=49
又a^2=b^2=1,a*b=1/2
故λ^2+9+λ*3=49
λ=-8或5