Let $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ be three vectors such that $\left|\overrightarrow{a}\right|=2, \left|\overrightarrow{b}\right|=1$ and $\left|\overrightarrow{c}\right|=3.$ If the projection of $\overrightarrow{b}$ along $\overrightarrow{a}$ is double of the projection of $\overrightarrow{c}$ along $\overrightarrow{a}$ and $\overrightarrow{b}, \overrightarrow{c}$ are perpendicular to each other, then the value of $\frac{{\left|\overrightarrow{a}-\overrightarrow{b}+2\overrightarrow{c}\right|}^2}{2}$ is equal to

• A

  $41$
• B

  $14$
• C

  $\sqrt{14}$
• Correct answer
  D

  $20.5$

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