The vector \( \hat{\mathrm{i}}+x \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \) is rotated through an an...
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0The vector \( \hat{\mathrm{i}}+x \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \) is rotated through an angle \( \theta \) and doubled in magnitude, then it becomes \( 4 \hat{i}+(4 x-2) \hat{j}+2 \hat{k} \). The values of \( x \) are
(1) \( -\frac{2}{3} \)
(2) \( \frac{1}{3} \)
(3) \( \frac{2}{3} \)
(4) 2
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