Vector Algebra

Let a unit vector which makes an angle of \(60^{\circ}\) with \(2 \hat{i}+2 \hat{j}-\hat{k}\) and an angle of \(45^{\circ}\) with \(\hat{i}-\hat{k}\) be \(\vec{C}\). Then \(\vec{C}+\left(-\frac{1}{2} \hat{i}+\frac{1}{3 \sqrt{2}} \hat{j}-\frac{\sqrt{2}}{3} \hat{k}\right)\) is: