Question

已知向量a=(cosα,sinα),向量b=(cosβ,sinβ) 若α-β=π/3,求a+2b向量的绝对值

Answer 1

|a+2b|^2=|a|^2+4a.b+|b|^2

|a|^2=1,|b|^2=1,

4a.b=4*(cosαcosβ+sinαsinβ)=4cosα-β=2

所以|a+2b|^2=4,|a+2b|=2