# Types of Vectors

There are 10 different types of vectors that are generally used in maths and science. To recall, vectors are the physical quantities which have magnitude as well as direction. The various vector types that are covered here are as follows.

## Types of Vectors List

There are 10 types of vectors in mathematics which are:

- Zero Vector
- Unit Vector
- Position Vector
- Co-initial Vector
- Like and Unlike Vectors
- Co-planar Vector
- Collinear Vector
- Equal Vector
- Displacement Vector
- Negative of a Vector

### Zero Vector

A zero vector is a vector when the magnitude of the vector is zero and the starting point of the vector coincides with the terminal point. In other words, for a vector \(\overrightarrow{AB}\) the co-ordinates of the point **A** are same as that of the point **B** then the vector is said to be a zero vector and is denoted by 0**.**

This follows that the magnitude of the zero vector is zero and the direction of such a vector is indeterminate.

### Unit Vector

A vector which has a magnitude of unit length is called a unit vector. Suppose if \(\overrightarrow{x}\) is a vector having a magnitude x then the unit vector is denoted by **x̂** in the direction of the vector \( \overrightarrow{x}\) and has the magnitude equal to 1.

∴ \( \hat{x} = \frac{\overrightarrow{x}}{|x|} \)

It must be carefully noted that any two unit vectors and must not be considered as equal because they might have the same magnitude but the direction in which the vectors are taken might be different and as to define a vector we need both magnitude and direction and these unit vectors might differ.

### Position Vector

If **O** is taken as reference origin and **A** is any arbitrary point in space then the vector \(\overrightarrow{OA}\) is called as the position vector of the point.

Position vector simply denotes the position or location of a point in the three-dimensional Cartesian system with respect to a reference origin.

### Co-initial Vectors

The vectors which have the same starting point are called as co-initial vectors.

The vectors \( \overrightarrow{AB} \) and \( \overrightarrow{AC}\) are called as co-initial vectors as they have the same starting point.

### Like and Unlike Vectors

The vectors having the same direction are known as like vectors. On the contrary, the vectors having the opposite direction with respect to each other are termed to be unlike vectors.

### Co-planar Vectors

Three or more vectors lying in the same plane or parallel to the same plane are known as co-planar vectors.

### Collinear Vectors

Vectors which lie along the same line or parallel lines are known to be collinear vectors. They are also known as parallel vectors.

### Equal Vectors

Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same.

These two vectors as shown are equal vectors as they have both direction and magnitude equal.

### Displacement Vector

If a point is displaced from position A to B then the displacement AB represents a vector \(\overrightarrow{AB}\) which is known as the displacement vector.

### Negative of a Vector

If two vectors are the same in magnitude but exactly opposite in direction then both the vectors are negative of each other. Assume there are two vectors **a** and **b, **such that these vectors are exactly the same in magnitude but opposite in direction then these vectors can be given by

**a **= – **b**