A non-zero vector \( \vec{a} \) is such that its projections along vectors \( \frac{i+j}{\sqrt{2... VIDEO
A non-zero vector \( \vec{a} \) is such that its projections along vectors \( \frac{i+j}{\sqrt{2}}, \frac{-i+j}{\sqrt{2}} \) and \( \hat{k} \) are equal, then unit vector along \( \vec{a} \) is
(1) \( \frac{\sqrt{2} \hat{j}-\hat{k}}{\sqrt{3}} \)
(2) \( \frac{\hat{j}-\sqrt{2} \hat{k}}{\sqrt{3}} \)
(3) \( \frac{\sqrt{2}}{\sqrt{3}} \hat{j}+\frac{\hat{k}}{\sqrt{3}} \)
(4) \( \frac{\hat{j}-\hat{k}}{\sqrt{2}} \)
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