A Detailed Study on Types of General Vector Notations

An object with magnitude and direction is called a vector. We can represent such a quantity mathematically or geometrically. 

A vector consists of initial points and terminal points represented by arrows. The arrow has a direction equal to that of the quantity. The arrow’s length is equal to the magnitude of that quantity.  

Vectors do not have positions, even though they have magnitude and direction. A scalar differs from a vector in that it has a magnitude but no direction. For example, acceleration, velocity, and displacement are vector quantities, while mass, time, and speed are scalars.

General notation of vectors

A vector is an object usually represented as an arrow over a letter. ‘Vector’ is a Latin word that means carrier. Physically, vectors are represented by directed line segments, each with an arrow denoting the vector’s direction and a length equal to the vector’s magnitude. The vector’s axis travels from tail to head.

Types of vectors

There are numerous types in which we can find and describe the vector. Each of them is unique, though easy to understand. They have specific properties to describe them.  

• Co-initial Vector

Co-initial vectors are a form of vector in which the beginning points of two or more distinct vectors are the same. All vectors in this sort of vector begin from the same point. We call these vectors co-initial vectors because their origin points are the same. 

• Collinear Vectors

The collinear vector is another vector in which two or more vectors, regardless of magnitude or direction, are parallel. Because they are parallel, they never cross paths.

• Null Vector

The zero vector is another vector in which the vector’s value is zero, and the origin and endpoint points of the vector are the same. The zero vector has no constituents and will not point in any direction.

1. Unit Vector

The unit vector is a subtype of a vector with a value based on the length of one unit. Unit vectors are any vectors with a magnitude of one.

• Position Vector

A position vector is a vector in which the origin point is set to O, and one random point in the space is designated as A. The position vector with the reference origin O is known as vector AO.  

• Coplanar Vectors

Coplanar vectors have three or more vectors in the same plane, or that can lie in the parallel plane. There is always the chance of finding any two different vectors in the same plane, referred to as coplanar vectors.

1. Unlike and Like Vectors 

Like vectors are the type of vectors that have the same direction, and we refer to them as such. Unlike vectors are vectors with the same direction but in opposite directions.  

• Equality of Vector

Equal vectors have two or more vectors with the same magnitude and direction are considered equal.

• Displacement Vector

The displacement vector is the vector that occurs when one vector shifts from its original position. The vector distance between the object’s starting and final points can determine the displacement.

• Negative Vector

A negative vector is a form where the value of both vectors is equal, but the direction of both vectors is opposite. Then we can write them as follows:  

a = -b 

This expression is known as a negative vector.  

Addition of Vectors

We represent vectors as a combination of direction and magnitude, and they are written with an alphabet and an arrow above them to indicate their direction and magnitude combinations. For example, we can put together p and q using vector addition, and we can express the resulting vector as p+q with an arrow above it.

Before we can learn about the characteristics of vector addition, we must first understand the operation should meet specific requirements. The most important condition is that we may combine vectors only if they are of the same type. For example, acceleration should be applied with simple acceleration, not mass.

Conclusion

In mathematics and physics, the vector is a quantity that has direction and magnitude. There are several different types of vectors. These are zero vector, unit vector, coinitial vectors, equal vectors and negative of a vector. In physics and mathematics, scalar has only magnitude and no direction. The scalar quantity is denoted as .