Question

已知向量a=(cosa,sina),向量b=(cosβ,sinβ),|a向量-b向量|=(2根号5)/5.

求cos（a-β）？

Answer 1

a-b=(cosa-cosb,sina-sinb)
|a-b|^2=(cosa-cosb)^2+(sina-sinb)^2
=2-2cos(a-b)
=4/5
cos(a-b)=3/5

Answer 2

a向量-b向量=(cosa-cosβ,sina-sinβ),
|a向量-b向量|=√[(cosa-cosβ)^2+(sina-sinβ)^2]=2√5/5.
(cosa-cosβ)^2+(sina-sinβ)^2=4/5.
2-2(cosacosβ+sinasinβ)=4/5
2-2cos（a-β）=4/5
cos（a-β）=3/5