Types of Vector

Vectors are geometrical entities with a magnitude and a direction that are used in geometry. A vector is represented by a line with an arrow pointing in the direction of the vector’s magnitude, and the length of the line represents the magnitude of the vector. Having stated that vectors are represented by arrows, it is important to note that they have both initial and terminal points. Over a period of 200 years, the concept of vectors evolved and matured. Vectors are used to represent physical quantities such as displacement, velocity, acceleration, and other similar quantities.

Aside from that, vectors have a wide variety of applications in physics and engineering. With the development of the field of electromagnetic induction in the late nineteenth century, the use of vectors became widespread.

A vector is a Latin word that literally translates as “carrier.” To get from point A to point B, vectors must be defined. The length of the line connecting the two points A and B is referred to as the magnitude of the vector, and the direction in which point A is displaced from point B is referred to as the direction of the vector AB, respectively. In physics, vectors play an important role in the calculation of forces. For example, vector quantities such as velocity, displacement, acceleration, and force all have a magnitude as well as a direction of application. Vectors are also referred to as Euclidean vectors or spatial vectors in some circles. Vectors have a wide range of applications in mathematics, physics, engineering, and a variety of other disciplines. 

Types of vectors

The vectors are classified into different types of vectors based on their properties, such as their magnitude, direction, and relationship with other vectors, which are described below. Various arithmetic operations and vector calculations are made easier with the help of these various types of vectors, which include the following:

Zero vectors

Vectors with zero magnitude are referred to as zero vectors, and they are denoted by the symbol 0~ = (0,0,0). The zero vector has no magnitudes and no direction, so it is called a zero vector. It is referred to as the additive identity of vectors in some circles.

Unit vectors

Unit vectors, denoted by the symbol a cap, are vectors whose magnitude is equal to one. It is referred to as the multiplicative identity of vectors in some circles. The unit vectors have a length of one. It is most commonly used to denote the direction of a vector in mathematics.

Position vectors

Three-dimensional space is represented by position vectors, which are used to determine the position and direction of movement of the vectors. In relation to other bodies, it is possible to change the magnitude and direction of position vectors. It is referred to as the location vector in some circles.

Equal vectors

When the corresponding components of two or more vectors are equal, two or more vectors are said to be equal. Equal vectors are vectors with the same magnitude and direction as one another. The initial and terminal points of each pair may differ, but the length and direction of each pair must be the same.

Negative vectors

When two vectors have the same magnitudes but are oriented in the opposite direction, they are said to be the negative of one another. Whenever two vectors A and B have the same length but the opposite direction, the vector A is said to be the negative of the vector B, and vice versa.

Parallel vectors

Parallel vectors are defined as two or more vectors that have the same direction but not necessarily the same magnitude when they are in the same plane. The angle formed by two parallel vectors is equal to one degree. Antiparallel vectors are vectors whose angles of direction differ by 180 degrees from one another; that is, antiparallel vectors have the opposite directions from one another.

Orthogonal vectors

When the angle between two or more vectors in space is 90 degrees, two or more vectors are said to be orthogonal. To put it another way, the dot product of orthogonal vectors is always equal to zero.

Conclusion

Vectors are geometrical entities with a magnitude and a direction that are used in geometry. A vector is represented by a line with an arrow pointing in the direction of the vector’s magnitude, and the length of the line represents the magnitude of the vector. In physics, vectors play an important role in the calculation of forces. Vectors are also referred to as Euclidean vectors or spatial vectors in some circles.

Vectors can be classified into several types, such as the zero vector, the unit vector, the co-initial vector, the position vector, the like-and-unlike vector, the collinear vector, and others.

The zero vector has no magnitudes and no direction, so it is called a zero vector. It is referred to as the additive identity of vectors in some circles.

Unit vectors, denoted by the symbol a cap, are vectors whose magnitude is equal to one. It is referred to as the multiplicative identity of vectors in some circles. 

Three-dimensional space is represented by position vectors, which are used to determine the position and direction of movement of the vectors.