If $\overrightarrow u,\overrightarrow v,\overrightarrow w$ are three vectors such that $|\overrightarrow u|=1,\:|\overrightarrow v|=2,\:|\overrightarrow w|=3$ and if the projection of $\overrightarrow v$ along $\overrightarrow u$ is equal to that of $\overrightarrow w$ along $\overrightarrow u$ and also if $\overrightarrow u$ and $\overrightarrow v$ are $\perp$ to each other, then $|\overrightarrow u-\overrightarrow v+\overrightarrow w|= ?$

Question

$\begin{array}{1 1} 14 \\ 7 \\ \sqrt {14} \\ \sqrt {7} \end{array}$