I am trying to solve for the X Y and Z coordinates of point given specific constraints. I am trying to setup 3 equations and 3 unknowns (the X Y and Z coordinates to solve this problem). I know equation of the plane that the rotation must follow, which is equation 1:

Ax + By + Cz = D (where I know the values of A B C and D)

The 2nd constraint that I know is the distance between the rotating point and the point I am trying to find, and this distance must always be the same. So I have a 2nd equation.

The 3rd constraint is that this point rotates about a pivot in the plane from equation 1. So my question is, how do I set up an equation which allows for a point to rotate about a point in a specific plane. In 2D this would be easy using sine and cosine, but in 3D I can't figure out how to do this. Thanks in advance for any help.