Dot Product Distributes over Addition/Proof 3

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

Setting $c = 1$ yields the result.