設向量a=(cosx,sinx),向量b=(cosy,siny),若|√2 a+b|=√3 |a-√2 b|,則cos(x-y)

設向量a=(cosx,sinx),向量b=(cosy,siny),若|√2 a+b|=√3 |a-√2 b|,則cos(x-y)

2a^2+2√2ab+b^2=3a^2+6b^2-2√6ab
a^2=1 b^2=1
6=(2√2+2√6)a·b
a·b=3(√6-√2)/4=cos(x-y)