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I am not familiar with defining a plane as such within solidworks. There is probably a way to do it, but I am unaware. How I would get around the problem is to create a 3d sketch with three points defining the plane. You can make each point coincident with two of the front top or right planes, then define the distance from the orign. These would be the a, b, and c. Next create the plane as reference geometry. Pick the three points you just created to fully define the plane. The plane can then be manipulated by changing the distances to the origin.
If you want to get the equation of an existing plane, the process is a little more involved. You will have to do the same process as before except make the distances from the origin driven. Then make the points coplanar with the face you wish to define. Read the dimensions to get the equation.
This procedure would be impractical for finding the equations for a number of planes. Maybe someone else has a better approach.