Vector Cross Product Distributes over Addition

Theorem
The vector cross product is distributive over addition.

That is, in general:


 * $\mathbf a \times \paren {\mathbf b + \mathbf c} = \paren {\mathbf a \times \mathbf b} + \paren {\mathbf a \times \mathbf c}$

for $\mathbf a, \mathbf b, \mathbf c \in \R^3$.