A vector is an ordered pair of numbers that can be used to describe a translation. The ordered pair gives both magnitude and direction.
You can express a vector as a ordered pair which called vector as algebraic representation. This number pair notation is called a column vector.
Vectors can also be represented as a line segment which called vector as geometrical representation. In this case, vectors are denoted by bold, italic type such as: vector u, vector AB, or underline type such as : vector u .
In such case vector AB, the order of letters is important because they give the direction of line. Vector AB is not the same as vector BA.
Equal vectors have same size (magnitude) and direction.
The operation on vectors can be considered both as algebraic representation and geometrical representation.
Here are Operation on Vectors.