Multiplication of a Vector by a Scalar

Multiplying a vector $\vec P$ by an ordinary number (a scalar) $s$ produces another vector,

The resulting vector $\vec Q$ has the same direction as $\vec P$ (for positive $s$) and a magnitude equal to $s$ times the magnitude of $\vec P$, i.e. $|\vec Q| = s|\vec P|$. If $s$ is negative, the direction of $\vec Q$ is reversed relative to $\vec P$ (this is exactly how a negative vector is produced, by multiplying by $s=-1$). If $s=0$, $\vec Q$ becomes the zero vector. This operation is the basis of finding the unit vector along a given vector: dividing $\vec M$ by its own magnitude $M$ is the same …