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Vector Multiplication

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:

Figure 1: Number and number line equivalency

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.

Figure 2: Squared number and number line equivalency

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

Figure 3: Number and number line equivalency

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

Figure 4: Redecoration of number line by adding a label $x$

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

Figure 5: Redecoration of number line by changing round marker to arrow

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

Figure 6: Redecoration of number line by adding a second perpendicular number line

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

Jonathan Bowen