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_数学解答

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

人气：130 ℃　时间：2020-05-02 05:44:37

解答

=Pai/3m*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3a*b=(2m+n)*(4m-n)=8m^2+2m*n-n^2=8+2-4=6a*b=|a||b|coscos=6/(2根号3*...