Unit vector `hat(P)` and `hat(Q)` are inclined at an angle `theta`. Prove that `|hat(P)-hat(Q)|= 2 sin(theta//2)`.

Explanation

We know that
`|vec A - vec B|^(2) = ( vec A - vec B). ( vec A - vec B)`
or `|vec A - vec B|^(2) = vec A . Vec A + vec B. vec B -2 vec A . Vec B`
`= 1 +1 -2 (1) 91) cos theta =2 91 - cos theta)` ltvbrgt `= [1 - (1-2 sin ^(2) theta //2 )] =4 sin ^(2) theta //2 `
`(:. cos 2 theta =1-2 sin ^(1) theta )`
`:. | vec A -vec B =2 sin theta //2`.