In mathematics, physics and engineering, a **Euclidean vector** or simply a **vector** (sometimes called a **geometric vector** or **spatial vector**) is a geometric object that has magnitude (or length) and direction.

Vectors can be added to other vectors according to vector algebra.

A Euclidean vector is frequently represented by a *ray* (a *directed line segment*), or graphically as an arrow connecting an *initial point* *A* with a *terminal point* *B*.

A vector is what is needed to “carry” the point *A* to the point *B*; the Latin word *vector* means “carrier”.

It was first used by 18th century astronomers investigating planetary revolution around the Sun.

The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from *A* to *B*.

Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity.

These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.