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The unit vector in \( \mathrm{ZOX} \) plane and making angles \( 45^{\circ} \) and \( 60^{\circ} \) respectively with \( \vec{a}=2 \hat{i}+2 \hat{j}-\hat{k} \) and \( \vec{b}=0 \hat{i}+\hat{j}-\hat{k} \),
(A) \( -\frac{1}{\sqrt{2}} \hat{i}+\frac{1}{\sqrt{2}} \hat{k} \)
(B) \( \frac{1}{\sqrt{2}} \hat{i}-\frac{1}{\sqrt{2}} \hat{k} \)
(C) \( \frac{1}{3 \sqrt{2}} \hat{i}+\frac{4}{3 \sqrt{2}} \hat{i}+\frac{1}{3 \sqrt{2}} \hat{k} \)
(D) none of these
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