Coordinates of a vector

Vectors are often represented as arrows on a line or a plane. The magnitude of the vector is represented by the length of the arrow, and its direction is represented by the direction the arrow points towards. If we equip the line or the plane with cartesian coordinates, we can represent the vector by the coordinates that the head of the arrow would have when placing its tail on the origin of the coordinate system.

For example, to represent on the plane a vector that has magnitude 10 and whose slope is four-thirds measured from the x-axis, we use the coordinates six eight(6,8).

Figure: Representation of a vector of magnitude 10 and slope 4/3 by its cartesian coordinates (6,8).