Vectors have two properties that make them very useful; specifically, magnitude (length) and direction. You will see moving forward how these two properties of vectors make them invaluable in game programming.

We will represent 2-dimensional vectors as an [x,y] value pair and 3-dimensional vectors as an [x,y,z] value pair.

What can we do with vectors you ask? Well, for starters we can add them together. Given two vectors A and B, we can add them together to get a vector C. The following picture illustrates this concept.

The green line represents vector A, the red line represents vector B, and the black line represents vector C. It is important to notice in this picture that the order in which we add the two vectors does not matter (A + B = B + A). This is called the commutative property.

Vectors can also be subtracted from one another:

The green line represents vector A and the red line represents vector B and the black line represents the new vector C. Here we have B - A. It is important to notice that the vector is drawn from the tip of A to the tip of B. If we were to subtract vector B from A, vector C would face the opposite direction. We can then state that vector subtraction is non-commutative.

A vector can be multiplied with a scalar value. For instance, say we have a 2-dimensional vector A = [3, 5] and we multiply it with the scalar value 2. Vector A is now twice as long and A = [6, 10]. If we wanted to reverse the direction of the vector we could multiply it with the scalar value -1. Two vectors can be multiplied together but I will save this for part two.

These are the most important basic properties of vectors. In the next tutorial I will explain the dot product, the cross product, vector length, and vector projection.

Continue to Vectors - part 2

Back to Main Page