The vector \(\vec{a}=-\hat{i}+2 \hat{j}+\hat{k}\) is rotated through a right angle, passing through the \(y\)-axis in it…

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 \(\vec{c}=5 \hat{i}+4 \hat{j}+3 \hat{k}\) is