# Vector Multiplication

Required Prerequisites- Standard Vectors

The material in this article has far ranging application but on its own may appear abstract. As you read through this article you should work to understand the concepts presented but temporarily suspend desires to apply them. This material serves as a foundation and a gateway that will add value each time you read it. We will explore the usefulness of each concept in deeper detail later.

## Squaring a Vector

Consider that we have the number $2$. We can also represent this number as a point on a number line. This is shown below graphically:

Suppose we multiply $2$ by itself to square it:

$$(2)(2) = 2^2 = 4$$

Once again, we can represent this squared number with a number line.

Let's return to back to our $2$ number line.

We can modify the number line by labeling it with "$x$". It's still just a number line.

Next, we can modify the number line by changing the marker from a dot to an arrow.

Finally, we can add a second number line perpendicular to the first and label it "$y$".

I'd like to emphasize, nothing has fundamentally changed. We've simply *decorated* our original number line.