Vectors In Maths: Definition, Types and Applications

Vectors are quantities consisting of magnitude and direction. The size of the vector is determined by its magnitude. It’s represented by a line with an arrow, with the length of the line representing the vector’s magnitude and the arrow indicating the direction. Force and velocity are the two examples of vectors.

When the magnitude and direction of two vectors are the same, they are equal. Vector is also known as Euclidean vector or Spatial vector. Vectors represent physical quantities such as displacement, velocity, and acceleration. This article has explained the definition of vector, their properties, formula, and types of vectors with examples.

Vectors In Maths: Definition

Vector is derived from the Latin word Vectus, meaning to carry. It is defined as the quantity consisting of magnitude and direction. Vectors represent the direction of objects from one position to another. The line segment of the vector is called magnitude, whereas the arrow indicates the direction. We can say that starting point is the tail and the ending point is the head.

The use of vectors is seen in mathematics and physics. The most commonly used vectors are force, velocity, acceleration, weight, momentum etc. For example, the vector starting from point A is called its initial point, and where it ends is called its terminal point. The distance between the initial and terminal points of a vector is called the magnitude of the vector. It is denoted as | |.

Vectors Examples

Velocity, Acceleration, Force, Increase/Decrease in Temperature are some of the most common vector examples. All of these quantities have magnitude and direction.

Types of Vectors

Some of the types of vectors are mentioned below:

Zero vector: The initial and terminal points coinciding with each other is called a zero vector.
Unit Vector: The vector whose magnitude is 1 unit is called a unit vector.
Coinitial Vector: Vectors having two or more same initial points are called coinitial vectors.
Collinear vectors: Vectors that are parallel to the same line irrespective of their magnitude and direction are called collinear vectors.
Equal Vectors: Vectors with the same magnitude and direction are called equal vectors regardless of their initial points.

Application

We need to understand the importance of using vectors for calculation purposes. Therefore, check the following applications as mentioned below:

Vectors are used in quantum mechanics.
It is used in oscillators.
It is used in vibration, sound and AC propagation.
It is used in the field of engineering.
It is used in gaming and designing roller coasters.
It is used to calculate force, torque and velocity.

Download NCERT Solution for Class 11 Maths Chapter 10 PDF

FAQ

The frequently asked questions on vectors are given below:

Q. What is a vector?
A. The vector is defined as a quantity having a magnitude and a direction.

Q. What are the examples of vectors?
A. The examples of vectors are force, velocity, acceleration, momentum etc.

Q. What are the types of vectors?
A. The types of the vector include zero, unit, coinitial, collinear and equal.

Q. What is the difference between scalar and vector?
A. The magnitude (size or measurement) of a scalar quantity is the same as the magnitude (size or measurement) of a vector quantity. Speed, for instance, is a scalar number, but velocity is a vector quantity.

Q. What is the magnitude of the vector?
A. The magnitude of the vector is denoted by the vertical line on both sides of the vector |a|.

We hope that you have got detailed information on vectors. Embibe provides CBSE Study Material that covers the whole CBSE Class 12 syllabus for Maths. You can also solve Maths Practice Questions for every chapter in the CBSE Class 12 syllabus for Maths that will also help you in your preparation of JEE as well.

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