Vectors in Space · Superchallenge problem

Let $\mathbf u = (1, 2, 3)$ and $\mathbf v = (2, 1, 0)$. Over all UNIT vectors $\mathbf w$, what is the largest possible volume of the parallelepiped spanned by $\mathbf u$, $\mathbf v$, $\mathbf w$?