Vector Cross Product Operator is Bilinear

Theorem
Let $\mathbf u$, $\mathbf v$ and $\mathbf w$ be vectors in a vector space $\mathbf V$ of $3$ dimensions:

where $\left({\mathbf i, \mathbf j, \mathbf k}\right)$ is the standard ordered basis of $\mathbf V$.

Let $c$ be a real number.

Then:
 * $\left({c \mathbf u + \mathbf v}\right) \times \mathbf w = c \left({ \mathbf u \times \mathbf w}\right) + \mathbf v \times \mathbf w$