The vector $\hat i+x\hat j+3\hat k$ is rotated about angle $\theta$ and is doubled in magnitude, then it becomes $4\hat i+(4x-2)\hat j+2\hat k$. The value of $x=?$

Question

$\begin{array}{1 1} (\frac{-2}{3},2) \\(\frac{1}{3},2) \\ (\frac{2}{3},0) \\ (2,7)\end{array}$