Let $\vec{a}$ be a vector which is perpendicular to the vector $3 \hat{i}+\frac{1}{2} \hat{j}+2 \hat{k}$. If $\vec{a} \times(2 \hat{i}+\hat{k})=2 \hat{i}-13 \hat{j}-4 \hat{k}$, then the projection of the vector $\vec{a}$ on the vector $2 \hat{i}+2 \hat{j}+\hat{k}$ is
