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

Question

( A ) $14$
( B ) $\sqrt{7}$
( C ) $2$
( D ) $\sqrt{14}$