Ray ray = new Ray (OriginOfRay.transform.position, player.transform.position)
and this is what happens:

How do I shoot the ray into the very center of the red box?
Thank you.
The constructor for Ray takes in origin and direction. Change your code to this and try:
Vector3 direction = player.transform.position - OriginOfRay.transform.position;
Vector3 origin = OriginOfRay.transform.position;
Ray r = new Ray(origin, direction);
Hope this helps.