Vectors:
A vector can be described as a quantity having magnitude and direction both.
Geometrically a vector can be represented by a directed line segment as shown in adjacent figure. The direction can be indicated by the length of the segment AB. A is called as initial point and B the terminal point of vector 
.
The line l of which the segment AB is a part, is called as line of support. The length is represented by 
The scalar is quantity, having magnitude only. Or we can say that a scalar is just a real number.
Displacement, velocity, momentum, area are some of the examples of vectors while distance, volume, speed, temperature are just scalars quantities.
Free vectors:
Vectors that are fully characterized by magnitude and direction only are called as free vectors and those which are fully characterized by magnitude, direction and also line of support are called as line vectors.
Displacement, velocity are free vectors while force and moment of a force about the point are line vectors.
Free Vector: A free vector cannot be located in any particular position. If a free vector 
can be represented by 
, it can equally be represented by 
, where OP and AB are equal in length and are in same direction (that is = ).
AB = OP = ||
Also AB is in same direction as OP.
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