Vector Algebra

Let \(\overrightarrow a\) be a vector which is perpendicular to the vector \(3\widehat i + {1 \over 2}\widehat j + 2\widehat k\). If \(\overrightarrow a \times \left( {2\widehat i + \widehat k} \right) = 2\widehat i - 13\widehat j - 4\widehat k\), then the projection of the vector \(\overrightarrow a\) on the vector \(2\widehat i + 2\widehat j + \widehat k\) is :