Definition:Scalar Multiplication/Vector Quantity

Definition
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 $\mathbf a$.