Unit vector making given angles with given vectors

1. A.
   $\frac{11}{2}$
2. B.
   $\frac{5}{2}$
3. C.
   9
4. D.
   7

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1. A.
   $- \frac{\sqrt{2}}{3}\widehat{i} + \frac{\sqrt{2}}{3}\widehat{j} + \left( \frac{1}{2} + \frac{2\sqrt{2}}{3} \right)\widehat{k}$
2. B.
   $\frac{\sqrt{2}}{3}\widehat{i} + \frac{1}{3\sqrt{2}}\widehat{j} - \frac{1}{2}\widehat{k}$
3. C.
   $\left( \frac{1}{\sqrt{3}} + \frac{1}{2} \right)\widehat{i} + \left( \frac{1}{\sqrt{3}} - \frac{1}{3\sqrt{2}} \right)\widehat{j} + \left( \frac{1}{\sqrt{3}} + \frac{\sqrt{2}}{3} \right)\widehat{k}$
4. D.
   $\frac{\sqrt{2}}{3}\widehat{i} - \frac{1}{2}\widehat{k}$

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