Introduction to Types of Vectors

The vector is defined as the quantity that has both magnitude and direction. The vectors are represented by the direct pointed line in which the length represents the vector and magnitude and the orientation represents the direction of the vector. The vector is used in mathematics and there are several types of vectors that include zero vector, unit vector, co-initial vector, collinear vector, equal vector, negative vector, and many more. Vectors are used to represent the physical objects as they have both magnitudes as well as direction.

Top 10 Types of Vectors

There are different types of vectors. Some of them are described below:

1. Co-initial Vectors

The co-initial vectors are the type of vectors in which two or more than two separate vectors have the similar initial points. In this type of vector, all vectors originate from the same position. The origin point is the same for the vectors and are called co-initial vectors. For example, if we have two AB→ and AC→ then these vectors are called as co-initial vectors as they both have a similar initial point that is A.

In the above diagram, the co-initial vectors are represented.

2. Collinear Vectors

The collinear is the other type of vector in which there are two or more than two vectors are parallel to each other irrespective of the magnitude or the direction. The parallel in nature means they never intersect with each other. The direction of both vectors is the same in nature. For example, if vector a is in x-direction and b is also in the same direction then they are known as collinear vectors. The coordinates of both vectors are the same in nature. The other property of collinear vector is that the cross product of both the collinear vectors is always equal to zero. The other name for the collinear vectors is parallel vectors.

In the above diagram, the two vectors are shown one in red color and the other one is in blue color. Both the vectors are known as collinear vectors.

3. Zero Vector

The zero vector is another type of vector in which the vector magnitude is equal to zero and the origin point of the vector coincides with the terminal point. For example, if the vector AB-> if the coordinates of A and the coordinates of B are the same then the vector is known as zero vector. The direction of the zero vector is indeterminate and the magnitude is always zero. The zero vector does not point in any direction and also has all components equal to zero.

In the above diagram, the zero vector is shown above.

4. Unit Vector

The unit vector is the type of vector that has the magnitude equal to the unit length that is one. All the vector having magnitude equal to one are known as unit vectors. Suppose there is vector x-> that is having the magnitude x then the unit vector is shown by x̂ that has the same direction of vector x and magnitude one.

The formula for the unit vector is given by:

The two vectors are not considered equal if they have the same magnitude until they both have the same direction also.

5. Position Vector

The position vector is another type of vector in which the origin point is taken as 0 and there is one arbitrary point named as A in the space. Then vector OA-> is known as the position vector having the reference origin 0. The position vector is mainly used for denoting the location or the position of the point in the 3D dimension Cartesian system. And the position is determined from any reference origin.

6. Co-planar Vectors

The co-planar vectors are the type of vectors in which three or more than three vectors lie in the same plane or can lie in the parallel plane then the vectors are known as coplanar vectors. There is always the possibility of finding any two random vectors lies in the same plane and known as the coplanar vectors. The other property for co-planar vectors is the scalar triple product for the three vectors is always equal to zero. The co-planar vectors are always linearly dependent vectors.

In the above diagram, the co-planar vectors are represented.

7. Like and Unlike Vectors

The like vectors are the type of vectors that are having the same direction and known as like vectors. The vectors that are having the opposite direction irrespective of each other are known as, unlike vectors.

8. Equal Vector

Equal vectors are the type of vector in which the two vectors or more than two vectors having the same magnitude as well as the same direction are known as equal vector.

In the above diagram the vectors AB-> and vector PQ-> are the equal vectors as they both have the same magnitude and same direction.

9. Displacement Vectors

The displacement vector is the type of vector when one vector is displaced from its position then the vector is known as the displacement vector. For example, if there is any object that is present at point A at time =0 and after some time it is at point B at time =t. The displacement can be calculated as the vector distance between the initial point of the object and the final point.

In the above diagram, the displacement is calculated as the length of the AB line in red color. The direction is from point A to point B.

10. Negative Vector

The negative vector is the type of vector in which the two vectors having an equal magnitude but the direction of both vectors is exactly opposite to each other. This type of vector is known as negative vectors. Suppose we have two vectors a and b which are negative vectors then it can be shown as

Conclusion

The vectors are the physical quantity that has the magnitude as well as the direction. The vectors are the mathematical concept and there are various kinds of vectors like collinear vectors, coplanar vectors, like and unlike vectors, displacement vector, unit vector, and many more defined above.