Types of Vectors:

We have discussed here different types of vectors with definitions and examples. It will help you understand the types of vectors.

Zero Vector or Null Vector:

A vector whose initial point and end point coincide is called a zero vector or null vector. The zero vector is denoted as \(\vec 0\). Zero vectors do not have any definite direction because it has zero magnitudes. The \(\overrightarrow {AA}\), \(\overrightarrow {BB}\), \(\overrightarrow {CC}\) etc are the zero vectors.

Unit Vector:

A vector whose magnitude is equal to 1 is called a unit vector. A unit vector is denoted by \(\hat a\), and the length of a unit vector is 1.

Co-initial Vectors:

A vector is called a co-initial vector if two or more vectors have the same initial point. For example, vectors OP and OR are co-initial vectors as their initial point O is the same.

Collinear Vectors:

A vector is called a collinear vector if two or more vectors are parallel to the same line, irrespective of their directions and magnitudes. The collinear vectors are also called parallel vectors.

Equal Vectors:

Two vectors \(\vec a\) and \(\vec b\) are called equal if they have the same direction and magnitude regardless of their initial point. Equal vectors are written as \(\vec a = \vec b\).

Negative Vectors:

A vector \(\vec A\) is called the negative vector of \(\vec B\) if the magnitude of both vectors is the same, but the direction of both the vectors is opposite. The negative vector is written as \(\vec A\) = - \(\vec B\).

Position Vectors:

A vector, whose one end is fixed and other end is in space, describes the position of the point in space relative to the fixed point. The position of the vector can change in length and direction as the point in space moves.

For example "O" is a fixed point, and "P" is any point in the space, then the position of P with reference to O is called position vector.

Like and Unlike Vectors:

The vectors having the same direction is called like vectors and the vectors having the opposite directions are called, unlike vectors, irrespective of their magnitude.

Coplanar Vectors:

The vectors which lie on the same plane, in a three-dimensional space are called coplanar vectors.