Definition:Scalar Multiplication/Vector Quantity

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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 $\mathbf a$.