Let $\bar{u}, \bar{v}, \bar{w}$ be vectors such that $|\bar{u}|=1,|\bar{v}|=2,|\bar{w}|=3$. If the projection of $\bar{v}$ on $\bar{u}$ is equal to that of $\bar{w}$ on $\bar{u}$, and the vectors $\bar{v}, \bar{w}$ are perpendicular to each other, then $|\bar{u}-\bar{v}+\bar{w}|=$

• A

  $2$
• B

  $\sqrt{7}$
• C

  $\sqrt{14}$
• Correct answer
  D

  $14$

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