Question

If `hata` and `hatb` are unit vectors, then prove that `|hata + hatb| = 2 cos  theta/2`, where θ is the angle between them.

Answer 1

`(hata + hatb).(hata + hatb) = |hata|^2 + |hatb|^2 + 2(hata.hatb)`

`|hata + hatb|^2 = 1 + 1 + 2costheta`

= `2(1 + cos theta) = 4cos^2  theta/2`

∴ `|hata + hatb| = 2cos  theta/2`