已知向量ab的夹角为30,|a|=根号3，|b|=1,求a+b与a-b的夹角

(a+b)(a-b) =a²-b² =|a|²-|b|² =3-1 =2 |a+b| =√(a+b)² =√(a²+2ab+b²) =√(3+2*√3*1*cos30°+1) =√7 |a-b| =√(a-b)² =√(a²-2ab+b²) =√(3-2*√3*1*cos30°+1) =1 (a+b)(a-b)=|a+b||a-b|cos夹角 cos夹角=(a+b)(a-b)