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A unit radial vector \( \hat{r} \) makes angles of \( \alpha=30^{\circ} \) relative to the \( x \)-axis, \( \beta=60^{\circ} \) relative to the \( y \)-axis, and \( \gamma=90^{\circ} \) relative to the \( z \)-axis. The vector \( \hat{r} \) can be written as :
(1) \( \frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j} \)
(2) \( \frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j} \)
(3) \( \frac{\sqrt{2}}{3} \hat{i}+\frac{1}{\sqrt{3}} \hat{j} \)
(4) None of these
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