Question to other math geeks out there:

If I have vectors u and v, it’s trivial to compute the cross product, u x v. Unfortunately, what I have is u x v and v, and I need u. Is there a property of cross products that allows one to determine one of the components, or to otherwise “solve for u”?

I know one definition of cross product is |u||v|sin q, but solving that isn’t going to work because I don’t know the angle, and I need the direction as well as magnitude.

Any suggestions?