Do the rays ba and ab define the same ray? in complete sentences, explain why the two rays are the same or why the two rays are not the same.

Rays are named according to their endpoints, the first one named is the "starting" endpoint, the second one is the one that will continue on into infinity.  Therefore, ray BA has a terminal endpoint at B and goes through point A into infinity.  Ray AB has a terminal endpoint at A and goes through point B into infinity.  Definitely NOT the same ray.