Dot Product Associates with Scalar Multiplication/Proof 1

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

Let $c$ be a real scalar.

Then:


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