Lines & Planes in Space · Superchallenge problem

Let $P_1 = (1, 2, 2)$, $P_2 = (2, 1, -2)$ and $P_3 = (2, -2, 1)$. For a plane $\Pi$ through the origin, let $S(\Pi)$ be the sum of the squares of the distances from $P_1$, $P_2$, $P_3$ to $\Pi$. Show that $S(\Pi)$ is the same for every such plane, and find it.