Types Of Vectors

The physical quantities which have magnitude as well as direction attached to them are known as vectors. The various types of vectors are,

  1. Zero Vector:

If the magnitude of the vector is zero and the starting point of the vector coincides with the terminal point i.e. 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 vector is indeterminate.

  1. Unit Vector:

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

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

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.

  1. 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.

  1. Co-initial Vectors:

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

Types of Vectors

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

  1. Like and Unlike Vectors:

The vectors having same direction are known as like vectors.
Whereas, the vectors having opposite direction w.r.t. each other are termed to be unlike vectors.

  1. 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:

 

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

  1. Equal Vectors:

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

Types of vectors

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

  1. 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.
  2. Negative of a vector:

If two vectors are 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 same in magnitude but opposite in direction then these vectors can be given by

 = – b

Moving forward, we will be learning about vectors in detail.  To learn more about vectors and its properties, visit our site BYJU’S.


Practise This Question

If a,b are unit vectors such that the vector a+3b is perpendicular to 7a5b and a4b is perpendicular to 7a2b,then the angle between a and b is