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