Vector Algebra

Let \(\overrightarrow u\), \(\overrightarrow v\) and \(\overrightarrow w\) be vectors in three-dimensional space, where \(\overrightarrow u\) and \(\overrightarrow v\) are unit vectors which are not perpendicular to each other and \(\overrightarrow u\) . \(\overrightarrow w\) = 1, \(\overrightarrow v\) . \(\overrightarrow w\) = 1, \(\overrightarrow w\) . \(\overrightarrow w\) = 4

If the volume of the paralleopiped, whose adjacent sides are represented by the vectors, \(\overrightarrow u\), \(\overrightarrow v\) and \(\overrightarrow w\), is \(\sqrt 2\), then the value of \(\left| {3\overrightarrow u + 5\overrightarrow v } \right|\) is ___________.