One way to define plane is by two non-colinear vectors and a base point.
p(u,v) = ↑r + u·↑a + v·↑b, where u,v are scalars
After doing the plane ray intersection you know the point of intersection with the plane ↑h, which by definition must lie on the plane. To get the values of u,v for that point you have to project the vector from ↑r to the intersection point onto the base vectors ↑a and ↑b:
u = (↑h - ↑r) · ↑a ; where '·' denotes the scalar product
v = (↑h - ↑r) · ↑b