Let O be the origin. Let $\overrightarrow{OP} = x\widehat i + y\widehat j - \widehat k$ and $\overrightarrow{OQ} = -\widehat i + 2\widehat j + 3x\widehat k$, $x, y \in R, x > 0$, be such that $|\overrightarrow{PQ}| = \sqrt{20}$ and the vector $\overrightarrow{OP}$ is perpendicular $\overrightarrow{OQ}$. If $\overrightarrow{OR} = 3\widehat i + z\widehat j - 7\widehat k$, $z \in R$, is coplanar with $\overrightarrow{OP}$ and $\overrightarrow{OQ}$, then the value of $x^2 + y^2 + z^2$ is equal to :