Question

已知a+b+c=0,且 lal =3,lbl =5 ,lcl =7,则向量a与b的夹角是多少?

Answer 1

(a+b+c)*(a+b+c) = |a|^2 + |b|^2 + |c|^2 + 2a*b + 2c*(a+b) = 0

3^2 + 5^2 + 7^2 + 2a*b + 2c*(-c) = 3^2 + 5^2 - 7^2 + 2a*b = 0

a*b = 15 = |a||b| cos = 3*5*cos

cos = 1

向量a与b的夹角 = 90 degree