If $a\hat{\mathrm{i}}+\hat{\mathit{j}}+\hat{\mathit{k}}, \hat{\mathit{i}}-b\hat{\mathrm{j}}+\hat{\mathit{k}}, \hat{\mathit{i}}+\hat{\mathit{j}}-c\hat{\mathit{k}}$ are coplanar, then $abc+2$ is equal to

Let $G$ be the centroid of the $∆ABC$ whose sides are of lengths $a, b$ and $c$. If $P$ be a point in the plane of $∆ABC$ such that $PA=1, PB=3, PC=4$ and $PG=2$, then the value of $a^2+b^2+c^2$ is