Let $\vec{a}-=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=\hat{i}--2 \hat{j}-\hat{k}$. Let a vector $\vec{v}$ be in the plane containing $\vec{a}$ and $\vec{b}$. If $\vec{v}$ is perpendicular to the vector $3 \hat{i}+2 \hat{j}-\hat{k}$ and its projection on $\vec{a}$ is 19 units, then $|2 \vec{v}|^2$ is equal to $\_\_\_\_$ .