We know that the vector product $a \times b$ of two vectors $a$ and $b$ is itself a vector quantity. Therefore we can multiply it by another vector $c$. The product $(a \times b).c$ is called scalar triple product, which is a pure number. On the other hand the product $a \times (b \times c)$ is called vector triple product, which is again a vector quantity.

The vector product of two vectors one of which is itself the vector product of two vectors is a vector quantity called a “triple cross product”.

$a \times (b \times c)$ = $(a . c)b – (a . b)c$