Let \( \vec{a} \) be a vector which is perpendicular to the vector \( 3\hat{i} + \tfrac{1}{2}\hat{j} + 2\hat{k} \). 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:
