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
external image 11a77539e7082a0ab934de189ee93215.png The Picture below shows us a graphic example of this.

external image 342px-Vector_AB_from_A_to_B.svg.png
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.
external image 300px-Vector_by_Zureks.svg.png

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 external image 9e100c62ab1b3b4e9229e0f2e985fb68.png
external image 619px-Position_vector.svg.png
The notion that the tail of the vector coincides with the origin is implicit and easily understood. Thus, the more explicit notation external image 0ba51574b8d84a80f2ed6c00af50ce40.png is usually not deemed necessary and very rarely used.