Vector Algebra: JEE Main 2004 Mathematics question

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