The vector \(\hat{i}+x \hat{j}+3 \hat{k}\) is rotated through an angle θ and doubled in magnitude, then it becomes \(4 \hat{i}+(4 x-2) \hat{i}+2 \hat{k}\). The value of x is
A. \(\left\{-\frac{2}{3}, 2\right\}\)
B. \(\left\{\frac{1}{3}, 2\right\}\)
C. \(\left\{\frac{2}{3}, 0\right\}\)
D. {2, 7}
Answer:A
The vector \(\hat{i}+x \hat{j}+3 \hat{k}\) is rotated through an angle θ and doubled in magnitude, then it becomes \(4 \hat{i}+(4 x-2) \hat{i}+2 \hat{k}\). The value of x is
A. \(\left\{-\frac{2}{3}, 2\right\}\) B. \(\left\{\frac{1}{3}, 2\right\}\) C. \(\left\{\frac{2}{3}, 0\right\}\) D. {2, 7}