Find the equation of the plane passing through the intersection of the planes $\vec{r} \cdot $2\hat{i} + 2\hat{j} - 3\hat{k}$ = 7$ and $\vec{r} \cdot $2\hat{i} + 5\hat{j} + 3\hat{k}$ = 9$ and through the point $(2, 1, 3)$.