Dot Product Distributes over Addition/Proof 3

Theorem
Let $\mathbf u, \mathbf v, \mathbf w$ be vectors in the vector space $\R^n$.

Then:


 * $\left({\mathbf u + \mathbf v}\right) \cdot \mathbf w = \mathbf u \cdot \mathbf w + \mathbf v \cdot \mathbf w$

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 $c = 0$ yields the result.