Dot Product Distributes over Addition/Proof 3

Proof
From Dot Product Operator is Bilinear:
 * $\left({c \mathbf u + \mathbf v}\right) \cdot \mathbf w = c \left({\mathbf u \cdot \mathbf w}\right) + \left({\mathbf v \cdot \mathbf w}\right)$

Setting $c = 1$ yields the result.