Vectors

In elementary mathematics, physics, and engineering, a **vector** is a geometric object that has both a magnitude (or length), direction and sense, i.e., orientation along the given direction. A vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an **initial point** //A// with a **terminal point** //B//, and denoted by The Picture below shows us a graphic example of this.

The magnitude of the vector is the length of the segment and the direction characterizes the displacement of //B// relative to //A//: how much one should move the point //A// to "carry" it to the point //B//.

__Example of Vectors__

Vectors are fundamental in the physical sciences. They can be used to represent any quantity that has both a magnitude and direction, such as velocity, the magnitude of which is speed. For example, the velocity //5 meters per second upward// could be represented by the vector (0,5). Vectors also describe many other physical quantities, such as displacement, acceleration, momentum, and angular momentum. Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field.

__Column Vector__

Vectors in an //n//-dimensional Euclidean space can be represented in a Cartesian coordinate system. The endpoint of a vector can be identified with an ordered list of //n// real numbers. As an example in two dimensions (see figure), the vector from the origin //O// = (0,0) to the point //A// = (2,3) is simply written as The notion that the tail of the vector coincides with the origin is implicit and easily understood. Thus, the more explicit notation is usually not deemed necessary and very rarely used.