Question

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

Answer 1

The first plane has unit normal vector `mathbf u =1/sqrt26 <4,-3,1>`. That and `- mathbf 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.

I think there may be a misunderstanding in your question.