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 :

Question

( A ) $\{2, 7\}$
( B ) $\{ -\frac{2}{3}, 0 \}$
( C ) $\{ \frac{1}{3}, 2 \}$
( D ) $\{ -\frac{2}{3}, 2 \}$