For $\mathbf{x}=\left(x_1, x_2, x_3\right) \in \mathbb{R}^3$, define $|\mathbf{x}|=\sqrt{x_1^2+x_2^2+x_3^2}$. For $\mathbf{a}=(1,4,4)$ and $\mathbf{b}=$ $(1,0,1)$, the maximum value of $|\mathrm{x}|$ satisfying $|\mathrm{x}-\mathrm{a}|=2|\mathrm{x}-\mathrm{b}|$ is

• A

  $\frac{5}{3}$
• Correct answer
  B

  $5$
• C

  $\frac{\sqrt{13}}{3}+5$
• D

  $\frac{2 \sqrt{13}}{3}+5$

Hence, the correct answer is option: 'B'.