Find the equation of the plane through the point $(2,5,7)$ that is parallel to the line $\mathbf{r} = (3\mathbf{i} + 2\mathbf{j} - 2\mathbf{k}) + t(\mathbf{i} + 2\mathbf{j} + 2 \mathbf{k})$ and perpendicular to the plane $4x + 5y + 6z = 14$. Write the equation in the form indicated.

Equation: $(x - 2) +$ $(y -$) $-\,3(z -$)$= 0$