A vector is a mathematical object represented by an ordered list of numbers called components, which define its magnitude and direction in a multi-dimensional space. Vectors can be added, subtracted, and scaled by a scalar, following specific rules.

For example, in a two-dimensional (2D) Cartesian plane, a vector has two components: representing its horizontal displacement and representing its vertical displacement. Similarly, in a three-dimensional (3D) Euclidean space, a vector has three components: , , and .

Vectors can be represented graphically as arrows pointing from the origin to the point defined by their components. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents its direction.