A vector determined by a segment oriented **AB** is the set of all geared segments **AB**.

If we indicate with this set, symbolically we can write:

= {**XY**/**XY **~ **AB**}

Where **XY** is any segment of the set.

The vector determined by **AB** is indicated by or **B - A** or .

Same vector is determined by an infinity of oriented segments called *representatives* of this vector, and all equipolent with each other. Thus, a segment determines a set that is the vector, and any of these representatives determines the same vector.

Using our capacity for abstraction a little more, if we consider all the infinite oriented segments of common origin, we are characterizing, through representatives, the totality of the vectors of space. Now each of these segments is a representative of a single vector. Consequently, all vectors are represented in that set that we imagine.

The characteristics of a vector are the same as any of its representatives, that is: the *module*, a *direction* it's the * sense* of the vector are the module, direction and direction of any of its representatives.

The module of is indicated by || .

Next: Some Types of Vectors