The vector \( \vec{a}=-\hat{i}+2 \hat{j}+\hat{k} \) 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 \( \vec{c}=6 \hat{i}+4 \hat{j}+3 \hat{k} \) is
