The vector \( \vec{a} = -\hat{\imath} + 2\hat{\jmath} + \hat{k} \) is rotated through a right angle, passing through the y-axis in its way and the resulting vector is \( \vec{b} \). Then the projection of \( 3\vec{a} + \sqrt{2}\,\vec{b} \) on \( \vec{c} = 5\hat{\imath} + 4\hat{\jmath} + 3\hat{k} \) is:
