A vector is a line segment oriented by an arrowhead drawn at one of its ends:

Point A is called **origin** and the point of the arrow (B) is called **extreme **vector.

All vectors consist of the following elements:

- Magnitude or modulus: is the length or size of the segment.
- Direction: is the direction of the line that contains the vector or any line parallel to it.
- Direction: indicated by the arrowhead (end), it indicates to which side of the line of action the vector is directed.

**Vector types**

**Null Vectors**

They are those whose module is zero (0) and cannot be assigned an address or meaning. The end and origin of these vectors lie at the same point.

**Example**: Sean ** A** y

**two vectors that have the same module and the same direction, but different sense. When making a sum of both vectors, we obtain a null vector.**

*B*We know that:

** B **= –

*A*Thus:

** A** +

**=**

*B***+ (-**

*A***) =**

*A***-**

*A***=**

*A*

*0***Unit Vectors**

They are those vectors that have unit (1) as a module. They are generally denoted with a circumflex accent (commonly called a “little hat”), “^”.

**Example:** Vectors associated with the directions of the Cartesian coordinate axes x, y, z, are generally designated by the unit vectors î, ĵ, k.

**Team or equal vectors**

Another vector that has the same modulus and the same direction and sense is called an equipment vector of a given one.

**Opposite vectors**

Another vector that has the same modulus and the same direction, but opposite sense is called the opposite vector of a given one.

**Example**:

The opposite is

The opposite vector is - ** A** = (-A

_{x}, -TO

_{y}), that is to say:

** A **= –

*A***Concurrent or Angular Vectors**

They are those vectors whose directions or lines of action pass through the same point. They are also called angular because they form an angle between them.

** A**,

**y**

*B***are concurrent**

*C***Collinear Vectors**

They are those vectors that share the same line of action, that is, if they are parallel to a line or are on the same line.

Two vectors ** A** = (A

_{x}, TO

_{y}, TO

_{z}) Y

**= (B**

*B*_{x}, B

_{y}, B

_{z}) are collinear if:

- The relationships of its coordinates are the same.

( TO_{x} / B_{x} ) = (A_{y} / B_{y} ) = (A_{z} / B_{z} )

- The vector product of both vectors is null (zero), that is:

** A** ×

**= (A**

*B*_{y}B

_{z }- TO

_{z}B

_{y}) î + (A

_{x}B

_{z }- TO

_{z}B

_{x}) ĵ + (A

_{x}B

_{y }–

_{ }A

_{y}B

_{x}) k = 0

OR

** A** ×

**= |**

*B***| |**

*A***| sinθ = 0**

*B*Since θ = 0 or θ = 180 ⁰ (remember that θ is the angle between both vectors).

**Coplanar Vectors**

They are those vectors whose lines of action are located in the same plane, that is, if they are parallel to the same plane or are in the same plane.

** A**,

**y**

*B***are coplanar vectors**

*C*