Determining 3D position of point from 2D projection.

Question

Say I have a 3D point $p$ and I project this point (using perspective projection) onto the image plane at 2D point $u$. Knowing that $p$ is on a plane with gradient $(a,b,c)^T$, how can I express the coordinates of $p$ using the coefficients of the plane?$$$$Let me add some more detail. I know that f is my focal distance and that $p_1 = \frac{u_1p_3}{f}$ and $p_2 = \frac{u_2p_3}{f}$ but of course I am trying to express $p$ without using reference to its members and only the gradient and focal point and $u$.