Question

If `vec"a", vec"b"` are unit vectors and q is the angle between them, show that 

`tan  theta/2 = |vec"a" - vec"b"|/|vec"a" + vec"b"|`

Answer 1

We have `sin  theta/2 = 1/2|vec"a" - vec"b"|`

`cos  theta/2 = 1/2|vec"a" + vec"b"|`

`(sin  theta/2)/(cos  theta/2) = (1/2|vec"a" - vec"b"|)/(1/2|vec"a" + vec"b"|)`

`tan  theta/2 = |vec"a" - vec"b"|/|vec"a" + vec"b"|`