The vector is rotated through an angle and doubled in magnitude

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

The vector

\hat{i} + x\hat{j} + 3\hat{k}

is rotated through an angle

\theta

and doubled in magnitude, then it becomes

4\hat{i} + (4x-2)\hat{j} + 2\hat{k}

. The value of

x

are (1)

\left\{-\frac{2}{3}, 2\right\}

(2)

\left\{\frac{1}{3}, 2\right\}

(3)

\left\{\frac{2}{3}, 0\right\}

(4)

\left\{2, 7\right\}