A plane \(P\) contains the line of intersection of the plane \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=6\) and \(\vec{r} …

A plane \(P\) contains the line of intersection of the plane \(\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=6\) and \(\vec{r} \cdot(2 \hat{i}+3 \hat{j}+4 \hat{k})=-5\). If \(P\) passes through the point \((0,2,-2)\), then the square of distance of the point \((12,12,18)\) from the plane \(P\) is

[JEE Main 2023, 6 Apr (Shift 2)]