已知向量2a+b=(0,-5,10),c=(1,-2,-2),a*c=4,|b|=12,则=

题目

已知向量2a+b=(0,-5,10),c=(1,-2,-2),a*c=4,|b|=12,则=
= 这个是一个度数啊 答案是120°

答案

(2a+b)*c = (0,-5,10) * (1,-2,-2)
2a*c+b*c = -10
b*c = -18
|c| = (1^2 + (-2)^2 + (-2)^2)^0.5 = 3
cos = b*c/( |b|*|c|) = -18/(12*3) = -1/2;
= 120°