I have three points in space, which cannot move relative to one another, and create a reference plane.
There is a forth point, that lays off/on the plane (off will be more general solution, on will be a private case I guess).
How can I use the information I just described to predict where the point off/on the plane will lie when the plane moves? The point is constrained by the original relationship.
For example: $P_1$, $P_2$, $P_3$ define a plane and they are respectively $(1,1,5) , (0,1,5) , (-1,0,5)$.
The fourth point $P$ is $(-5,2,5)$ on the plane defined by $P_{1,2,3}$. What would be the coordinates of $P$ when the plane moves (arbitrary rotation in space) and $P_{1,2,3}$ have new values. In the example all points are on the same $z$ plane $(5)$ in the initial reference state.
Thanks!