In the relations you have shown, what are the operations? Are yu multiplying the magnitudes of the vectors, taking the dot-product, what?
It is an arbitrary vector then? (Since the choice of origin is arbitrary.) Therefore there is no reason that the rays should be in a plane defined by the incedent ray and some arbitrary vector unless the origin is in some special place.
This sort of setup is normally used when you want to invoke the principle of least time.
I don't have that one. You should double-check the context that he's doing this in.