A vector is a quantity with magnitude and direction, and magnitude of a vector is known as length. Vector is represented by a directed line segment. The direction of the vector is indicated by an arrow pointing from the tail to head. If tail is at point A and head is at point B then the vector from A to B is written $\vec{AB}$  

Examples: Acceleration, momentum, force magnetic field etc.

A vector is a combination of three things.
  1. Magnitude which is a positive number,
  2. Direction in space and
  3. The idea of direction.
A vector is represented by a straight line which will have an starting point and an ending point.
A two-dimensional vector will be an ordered pair of real numbers v = (a, b) where a and b are the components of v.

The length of the vector v = (a, b) is defined as |v| = v = $\sqrt{(a^{2} + b^{2})}$