Vectors and Their Types



  • Zero Vector
  • Unit Vector
  • Co-initial and Co-terminus Vectors
  • Equal Vectors
  • Negative of a Vector
  • Collinear Vectors
  • Free Vectors
  • Localised Vectors


Zero Vector: A vector whose initial and terminal points coincide, is called a zero vector (or null vector), and denoted as `vec 0` . Zero vector can not be assigned a definite direction as it has zero magnitude. Or, alternatively otherwise, it may be regarded as having any direction. The vectors `vec ("AA") , vec (BB)` represent the zero vector,

Unit Vector: A vector whose magnitude is unity (i.e., 1 unit) is called a unit vector. The unit vector in the direction of a given vector `vec a` is denoted by `hat a`.

Coinitial Vectors: Two or more vectors having the same initial point are called coinitial vectors.

Collinear Vectors: Two or more vectors are said to be collinear if they are parallel to the same line, irrespective of their magnitudes and directions.

Equal Vectors: Two vectors  are said to be equal, if they have the same magnitude and direction regardless of the positions of their initial points, and written as `vec a =vec b`.

Negative of a Vector: A vector whose magnitude is the same as that of a given vector , but  direction is opposite to that of it, is called negative of the given vector.
For example, vector `vec (BA)`  is negative of the vector `vec (AB)` , and written as `vec (BA) = - vec (AB)`.
Remark: The vectors defined above are such that any of them may be subject to its parallel displacement without changing its magnitude and direction. Such vectors are called free vectors. 

If you would like to contribute notes or other learning material, please submit them using the button below.

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1

Series 2 | Types of Vectors

Next video

Types of Vectors [00:23:57]

      Forgot password?
Use app×