# Introducing vectors

What is a vector? A vector is an n-tuple of numbers. It represents a displacement measured as a magnitude and a direction. Each element of a vector is usually expressed as a subscript, such as *(V*0*, V*1*, V*2*, … V*N*)*. In the context of games, vectors usually have two, three, or four components.

For example, a three-dimensional vector measures displacement on three unique axes: *x*, *y*, and *z*. Elements of vectors are often subscripted with the axis they represent, rather than an index. *(V*X*, V*Y*, V*Z*)* and *(V*0*, V*1*, V*2*)* are used interchangeably.

When visualizing vectors, they are often drawn as arrows. The position of the base of an arrow does not matter because vectors measure displacement, not a position. The end of the arrow follows the displacement of the arrow on each axis.

For example, all of the arrows in the following figure represent the same vector:

Each arrow has the same...