Prove $ u \cdot (u \times (\nabla \times u)) = 0 $ Prove $$ u \cdot (u \times (\nabla \times u)) = 0 $$
Where '$u$' is a 3D-velocity vector.
I came across this for a proof for converting Euler's Equation to the Bernoulli expression for a steady-state, in compressible fluid. 
Anyone know why this is the case? 

For simplicity, call ${\bf v} = \nabla \times {\bf u}$. The idea is that ${\bf u} \times {\bf v}$ is perpendicular to both ${\bf u}$ and ${\bf v}$, so that
$$
{\bf u} \cdot({\bf u} \times {\bf v}) = 0
$$
