Question

已知向量a=（cosx,sinx),b=(cosy,siny)若x-y=π/3,求|x+2b|

Answer 1

向量a=(cosx,sinx),向量b=(cosy,siny),

则a^2=1,b^2=1,

ab= cosx cosy+sinx siny

=cos(x-y)= cos(π/3)=1/2.

|a+2b|²= a^2 +4ab+4 b^2

=1+4*(1/2)+4=7,

∴|a+2b|=√7.