If , , prove that and are perpendicular.

If $\vec{a} = -\hat{i} - 2\hat{j} + 3\hat{k}$, $\vec{b} = 2\hat{i} + 3\hat{j} - 5\hat{k}$, prove that $\vec{a}$ and $\vec{a} \times \vec{b}$ are perpendicular.