Let \( \vec{u}, \vec{v} \) and \( \vec{w} \) be vectors in three-dimensional space, where \( \ve...

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

If the volume of the parallelopipede, whose adjacent sides are represented by the vectors then the value of is