# How do you find a unit vector perpendicular to 4i - 3j +k and parallel to the x-y plane?

The first plane has unit normal vector $m a t h b f u = \frac{1}{\sqrt{26}} < 4 , - 3 , 1 >$. That and $- m a t h b f u$ are the only unit vectors that are actually perpendicular to that plane.
Any vector in the form $< x , y , 0 >$ lies on or parallel to the x-y plane.