Let a unit vector which makes an angle of 60^° with 2 i +2 j - k and an angle of 45^° with i - k be C. Then C +(-1/2 i +1/(3 √ 2) j -(√ 2)/3 k ) is:

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