向量 已知|m|=1,|n|=2,(m,n)=π/3,a=2m+n,b=4m-n,求a与b的夹角的值

向量 已知|m|=1,|n|=2,(m,n)=π/3,a=2m+n,b=4m-n,求a与b的夹角的值
向量 已知|m|=1,|n|=2,(m,n)=π/3,a=2m+n,b=4m-n,求a与b的夹角的值

向量 已知|m|=1,|n|=2,(m,n)=π/3,a=2m+n,b=4m-n,求a与b的夹角的值
=Pai/3
m*n=|m||n|cosPai/3=1*2*1/2=1
|2m+n|=根号(4m^2+4m*n+n^2)=根号（4*1+4*1+4）=2根号3
|4m-n|=根号(16m^2-8m*n+n^2)=根号（16-8+4）=2根号3
a*b=(2m+n)*(4m-n)=8m^2+2m*n-n^2=8+2-4=6
a*b=|a||b|cos
cos=6/(2根号3*2根号3）=1/2
故向量a和b的夹角是60度.

(m,n)=π/3是啥意思呀？

不好意思恕我愚昧，(m,n)=π/3什么意思，我读这么久书还真没学过······