\begin{definition}[Definition:Scalar Multiplication/Vector Quantity]
Let $\mathbf a$ be a vector quantity.
Let $m$ be a scalar quantity.
The operation of scalar multiplication by $m$ of $\mathbf a$ is denoted $m \mathbf a$ and defined such that:
:the magnitude of $m \mathbf a$ is equal to $m$ times the magnitude of $\mathbf a$:
::$\size {m \mathbf a} = m \size {\mathbf a}$
:the direction of $m \mathbf a$ is the same as the direction of $\mathbf a$.
\end{definition}