Position vector \( \hat{k} \) is rotated about the origin by angle \( 135^{\circ} \) in such a w...

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Position vector \( \hat{k} \) is rotated about the origin by angle \( 135^{\circ} \) in such a way that the plane made by it bisects the angle between \( \hat{i} \) and \( \hat{j} \). Then its new position is
\( P \)
(1) \( \pm \frac{\hat{i}}{\sqrt{2}} \pm \frac{\hat{j}}{\sqrt{2}} \)
(2) \( \pm \frac{\hat{i}}{2} \pm \frac{\hat{j}}{2}-\frac{\hat{k}}{\sqrt{2}} \)
(3) \( \frac{\hat{i}}{\sqrt{2}}-\frac{\hat{k}}{\sqrt{2}} \)
(4) none of these
W
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