You need to understand what the equation of a plane tells you.
A plane is defined by a point on the plane (P0), and the normal vector to the plane(N). Thus any point on the plane X satisfies the constraint
If the normal vector has unit length, so it is normalized to have norm(N)==1, then the solution to your problem is trivial.
The distance to the plane is then simple. It is just:
If a point lies on the plane, then the distance to the plane is 0. And that is embodied in the equation of a plane that I gave above!
Finally, you might recognize that the above dot product is simply computed using the function dot, but even more simply written as a matrix multiply, if you have more than one point for which you need to compute this distance.