Let a unit vector which makes an angle of 60° with 2î + 2ĵ - k̂ and an angle of 45° with î - k̂ 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:
1
\(-\frac{\sqrt{2}}{3}\hat{i} + \frac{\sqrt{2}}{3}\hat{j} + \left(\frac{1}{2} + \frac{2\sqrt{2}}{3}\right)\hat{k}\)
2
\(\frac{\sqrt{2}}{3}\hat{i} + \frac{1}{3\sqrt{2}}\hat{j} - \frac{1}{2}\hat{k}\)
3
\(\left(\frac{1}{\sqrt{3}} + \frac{1}{2}\right)\hat{i} + \left(\frac{1}{\sqrt{3}}-\frac{1}{3\sqrt{2}}\right) \hat{j} + \left(\frac{1}{\sqrt{3}} + \frac{\sqrt{2}}{3}\right)\hat{k} \)
4
\(\frac{\sqrt{2}}{3}\hat{i} - \frac{1}{2}\hat{k}\)