Shortest distance between two points on a sphere

1. The problem statement, all variables and given/known data



See attached images.



2. Relevant equations



##\vec{A}⋅\vec{B} = AB \cos{\theta}##



3. The attempt at a solution


See attached images.



Is my answer correct? It looks a bit too messy.

Also, when finding the ##x-##...



Shortest distance between two points on a sphere

Shortest distance between two points on a sphere