Question

已知向量a=(cosα,sinα),b=(cosβ,sinβ),且la-bl=2根号5分之5,（1）求cos(α-β)的

Answer 1

a=(cosα,sinα),b=(cosβ,sinβ),la-bl=5/2√5

(1)

a.b = (cosα,sinα).(cosβ,sinβ)= cos(α-β)

a|^2+|b|^2 = (cosα)^2+(sinα)^2+(cosβ)^2+(sinβ)^2 =2

|a-b|^2 =(a-b).(a-b) =|a|^2+|b|^2 -2a.b

5/4 = 2 - 2cos(α-β)

cos(α-β) = 3/8