Vector triple product = 0

Question

Let $U, V, W$ be three non-zero vectors, no two of which are parallel.

Under what conditions is $U\times(V\times W) = 0$?

Answer 1

The construction $U\times(V\times W)$ will be zero if $U$ is collinear to $V\times W$.

Answer 2

The triple product will be zero if $U$ is perpendicular to the plane containing $V$ and $W$. This is equivalent to janmarqz' answer, but my answer doesn't assume that you know anything about $V \times W$.