How do I find the point equidistant from three points $(x, y, z)$ and belonging to the plane $x-y+3z=0?$ I struggle to find the point ${P}$ equidistant from the points ${A(1,1,1), B(2,0,1), C(0,0,2)}$ and belonging to the plane ${x-y+3z=0}$.
Any tips?

The line is perpendicular to the plane containing $A, B, C$. Transform the coordinates so the $ABC$ plane is the $x,y$-axis. Find the equidistant point on the $x,y$ plane. The line is the perpendicular to the plane at that point. Reverse the transform for that line.
