Given a normal vector of a $3D$ plane and a $x$-$y$ coordinates of a point on the plane with origin of the plane $(0, 0)$ being at $(0, 0, 0)$, how can I get $3D$ coordinates of the point?
Basically, I need to rotate a point on a plane with normal vector $(1, 0, 0)$ with respect to an arbitrary normal vector.
I really don't know even where to start. What should be the resulting algorithm. Should it be some sort of transformation matrix?