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:
