We have already talked about multiplying a vector by a regular number. For instance, if we multiply a vector $\vec A = (\text{magnitude } = 10 \text{ cm}, \text{ direction to East})$ by $5 \text{,}$ we will get another vector $\vec B$ that is $5$ times as long and in the same direction as $\vec A\text{.}$ We can write the resulting vector as $5 \vec A\text{.}$
On the other hand, if we multiply by $-5 \text{,}$ we will get a vector $\vec C \text{,}$ which is also $5$ times as long, but its direction will be opposite that of $\vec A \text{.}$
In the next sections, we will talk about multiplying two arbitrary vectors $\vec A$ and $\vec B\text{.}$ There are two different types of multiplication between two vectors, one results in a number and the other results in another vector.