Vector Algebra: JEE Main 2003 Mathematics question

Let $\overrightarrow u = \widehat i + \widehat j,\,\overrightarrow v = \widehat i - \widehat j$ and $\overrightarrow w = \widehat i + 2\widehat j + 3\widehat k\,\,.$ If $\widehat n$ is a unit vector such that $\overrightarrow u .\widehat n = 0$ and $\overrightarrow v .\widehat n = 0\,\,,$ then $\left| {\overrightarrow w .\widehat n} \right|$ is equal to :