Most spatial quantities are represented quantitatively by specifying the quantity relative to a coordinate system. The coordinate systems are specified using as many axes as there are dimensions. In a 2D space, two values are needed to specify the position of a point. For simplicity in text, the vector can also be represented as .
Vectors can represent directions.
In this case, the vector is usually a unit vector, that is, it has length 1. In this case, the length of the vector is the distance between the points. Such a space is called the vector space in which these vectors live. For example, vectors in the two-dimensional Cartesian plane like you've seen in introductory Physics courses have a first component that can be any real number and a second component that can also be any real number. A set of vectors from which you can construct any other vector in the space is called a spanning set .