Edit: No way to delete this thread?

Why would you want to delete it? And why not leave the original question? Even if you found the answer on your own, this thread could be useful to other people that might find it in the future...

I have an arbitrary surface normal and the normalized velocity of an object hitting the surface. Is there a way I can calculate the proper reflection vector without using trig operations?

It can be done using the dot product, like this:

reflected_vector = incident_vector - 2 * dot_product(incident_vector, normal) * normal