Let $\vec{m}$ be a vector of magnitude $\sqrt{3}$ and perpendicular to the vectors $\hat{i} + \hat{j}$ and $\hat{j} - \hat{k}$. Let $\vec{n}$ be another vector of magnitude $2\sqrt{6}$ and perpendicular to the vectors $2\hat{i} - \hat{j}$ and $\hat{j} + 2\hat{k}$. The area (in sq. units) of the triangle formed with $\vec{m}$ and $\vec{n}$ as sides is