Types of Vectors

The ten types of vectors are Unit Vector, Position Vector, Co-initial Vector, Like Vector, Unlike Vector, Coplanar Vector, Zero vector, Collinear Vector, Equal Vector, Displacement Vector, and Negative Vector.

Introduction

The vector is the quantity that combines the duo – magnitude and direction. Vectors are depicted by the direct pointed line in which the length shows the vector and magnitude, and the orientation shows the direction of the vector. They have initial points and terminal points and are represented by arrows. The advancement of the algebra of vectors and vector analysis as we know it was first revealed in sets of remarkable notes made by J. Willard Gibbs (1839-1903), also known as the Father of Vector Algebra. His notes were intended for his students at Yale University. 

Explain types of vectors

There are ten Types of Vectors given below- 

Zero Vector

In a zero vector, the magnitude of the vector is equal to zero, and the vector coincides with the terminal point, i.e., the starting point and the ending point of the vector are the same. For example, AB is a line segment, the coordinates of the point ‘A’ are the same as that of point ‘B.’ A zero vector is denoted by 0, and it doesn’t have any specific direction.

Unit Vector

Among the different kinds of vectors, The Unit vector, as the name ‘unit’ suggests, is the vector with a magnitude equal to 1. It is also known as the multiplicative identity of vectors. The length of these vectors is 1. We also consider that any two unit vectors should not be called equal because they can have the same magnitude, but the direction in which the vectors are taken might differ. The main purpose of a unit vector is to indicate direction.

Position Vector

These vectors are used to determine the position and direction of movement of the vectors in a three-dimensional space. Here, the origin point is taken as 0, and there is one arbitrary point named P in the space. The vector OP-> is known as the position vector having the reference origin 0. The location or position of the point is mainly denoted by the vector.

Co-initial Vector

Co-initial vectors have a common origin point, and they may scatter in different directions. For example, AB and AC are co-initial vectors since they have the same beginning point, ‘A.’ They are also called concurrent vectors.

Like Vector and Unlike Vector

The types of vectors having the same direction are called Like vectors. Alternatively, unlike vectors, the vectors have the opposite direction concerning each other. 

Co-Planar Vector

Co-Planar vectors are three or more vectors that lie in the same plane or are parallel to the same plane. Sometimes, there is the possibility of finding any two vectors lying in the same plane. The scalar triple multiplication for the three vectors always equals zero, and they are always linearly dependent vectors. 

Collinear Vector

It is the type of vector in which two or more vectors parallel to each other, disregarding the magnitude or direction. They never intersect with each other. For instance, if the vector ‘P’ is in the ‘A’-direction, and ‘Q’ is also in the same direction, they are collinear vectors. Their coordinates are the same. Another name for collinear vectors is Parallel vectors. 

Equal Vector

Equal Vectors have similar corresponding components. They own the same magnitude and direction, and their initial and terminal points might differ, but the length and direction must be identical.

Displacement Vector

When one vector is displaced from its place, the type of vector is known as the displacement vector. For instance, if some object is present at point ‘P’ at time =0 and afterward it is at point ‘R’ at time =t. The displacement can be determined as the vector distance between the starting point of the object and the ending point.

Negative Vector

A type of vector in which the two vectors with an equal magnitude but opposite direction are called negative vectors. If we take two negative vectors, ‘P’ and ‘R,’ It can be shown by P = -R. 

Conclusion

We saw here that there are ten types of vectors — the physical quantity, with the magnitude and direction. They are mathematical concepts, and there are different types of vectors, as discussed above. Vectors represent displacement, velocity, and acceleration and help define the force applied on a body simultaneously in the three dimensions.