Let a be a vector which is perpendicular to the vector 3 i +1/2 j +2 k. If a ×(2 i + k )=2 i -13 j -4 k, then the projection of the vector a on the…

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