Dot Product Associates with Scalar Multiplication

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

Let $c$ be a real scalar.

Then:
 * $\paren {c \mathbf u} \cdot \mathbf v = c \paren {\mathbf u \cdot \mathbf v}$