|a|=3,|b|=4,|a|与|b|的夹角为60度,求a+b与a-b的夹角的余弦值上面字母均为向量

Question

|a|=3,|b|=4,|a|与|b|的夹角为60度,求a+b与a-b的夹角的余弦值
上面字母均为向量

Answer 1

a*b=|a|*|b|*cos(π/3)=3*4*(1/2)=6
|a+b|^2
=(a+b)^2
=|a|^2+2a*b+|b|^2
=9+12+16
=37
|a-b|^2
=(a-b)^2
=|a|^2-2a*b+|b|^2
=9-12+16
=13
cos
=[(a+b)*(a-b)]/[|a+b|*|a-b|]
=(|a|^2-|b|^2)/[|a+b|*|a-b|]
=(9-16)/(√13*√37)
=-7/√481