1. Definition
Geometrically, a vector is an arrow having the three following characteristics :
- a direction (the line that contains it)
- a sense (top, right, bottom, left)
- a length (also called norm)
In Figure 5.1, we have the following :
- →a et →c are equal. →a=→c. The coordinates are : →c=(32).
- →a et →b have the same direction, the same length but an opposite sense. →a=−→b.
- →d et →e have the same direction, the same sense, but a different length. →d=2→e.

2. Addition
The addition of two vectors is defined as follows :
Geometrically, the sum of two vectors is obtained by putting them end to end, as showed in Figure 5.2. This is the so-called parallelogram law.
Example I

3. Subtraction
The vector subtraction is nothing but adding a vector whose sense is reversed.
Example II

4. Multiplication by a scalar (number)
A vector multiplied by a scalar gives another vector. It is is defined as follows :
Example III

Recapitulation
Geometrically, a vector is an arrow having a direction, a sense and a length. Two vectors are equal if they have those same characteristics or, in other words, if they have the same coordinates.
Geometrically, a vector can been seen as a point. The concept of vector generalizes the concept of point.
If two vectors have the same direction, then they are multiples of one another, like →d and →e in Figure 5.4. In that case, they are said to be collinear or, more generally, linearly dependant.
More generally, a vector is an algebraic and abstract concept which is beyond the scope of the present course.