JEE Exam  >  JEE Notes  >  Mathematics (Maths) for JEE Main & Advanced  >  Types of Vectors

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced PDF Download

A vector has direction and magnitude both but scalar has only magnitude. 

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

  • Magnitude of a vector a is denoted by |a| or a. It is non-negative scalar.
  • Direction of a vector is the angle made by the vector with the horizontal axis, that is, the X-axis. The direction of a  vector formula is related to the slope of a line. We know that the slope of a line that passes through the origin and a point (x, y) is y/x. We also know that if θ is the angle made by this line, then its slope is tan θ, i.e., tan θ = y/x. Hence, θ = tan-1 (y/x). 

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

Equality of Vectors

Two vectors a and b are said to be equal written as a = b, if they have (i) same length (ii) the same or parallel support and (iii) the same sense.

Types of Vectors

(i) Zero or Null Vector

A vector whose initial and terminal points are coincident is called zero or null vector. It is denoted by 0.
Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

(ii) Unit Vector 

A vector whose magnitude is unity is called a unit vector which is denoted by nˆ

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

(iii) Negative of a Vector 

A vector having the same magnitude as that of a given vector a and the direction opposite to that of a is called the negative of a and it is denoted by —a.

(iv) Like and Unlike Vectors 

Vectors are said to be like when they have the same direction and unlike when they have opposite direction.
Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

(v) Collinear or Parallel Vectors 

Vectors having the same or parallel supports are called collinear vectors.
Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

(vi) Coinitial Vectors 

Vectors having same initial point are called coinitial vectors.
Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

(vii) Localized Vectors 

A vector which is drawn parallel to a given vector through a specified point in space is called localized vector.

(viii) Coplanar Vectors 

A system of vectors is said to be coplanar, if their supports are parallel to the same plane. Otherwise they are called non-coplanar vectors.

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

Example: In the figure given below, identify Collinear, Equal and Coinitial vectors:

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

Solution: By definition, we know that

  • Collinear vectors are two or more vectors parallel to the same line irrespective of their magnitudes and direction. Hence, in the given figure, the following vectors are collinear: Types of Vectors | Mathematics (Maths) for JEE Main & Advanced
  • Equal vectors have the same magnitudes and direction regardless of their initial points. Hence, in the given figure, the following vectors are equal: Types of Vectors | Mathematics (Maths) for JEE Main & Advanced
  • Coinitial vectors are two or more vectors having the same initial point. Hence, in the given figure, the following vectors are coinitial: Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

Example: In the given figure, identify the following vectors

  1. Coinitial
  2. Equal
  3. Collinear but not equal

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

Solution:

  • Coinitial vectors have the same initial point. In the figure given above, vectors Types of Vectors | Mathematics (Maths) for JEE Main & Advanced  are the two vectors which have the same initial point P.
  • Equal vectors have same magnitudes and direction. In the figure given above, vectors Types of Vectors | Mathematics (Maths) for JEE Main & Advanced are equal vectors. 
  • Collinear vectors are two or more vectors parallel to the same line. In the figure given above, vectors  Types of Vectors | Mathematics (Maths) for JEE Main & Advancedare parallel and hence, collinear. Also,  vectors Types of Vectors | Mathematics (Maths) for JEE Main & Advanced are parallel and hence, collinear. We know that vectors Types of Vectors | Mathematics (Maths) for JEE Main & Advanced are also equal. Hence, vectors Types of Vectors | Mathematics (Maths) for JEE Main & Advancedare collinear but not equal.

The document Types of Vectors | Mathematics (Maths) for JEE Main & Advanced is a part of the JEE Course Mathematics (Maths) for JEE Main & Advanced.
All you need of JEE at this link: JEE
209 videos|443 docs|143 tests

Up next

FAQs on Types of Vectors - Mathematics (Maths) for JEE Main & Advanced

1. What are the different types of vectors based on direction?
Ans. Vectors can be classified into three types based on direction: collinear vectors, coplanar vectors, and concurrent vectors.
2. How are unit vectors defined in the context of vectors?
Ans. Unit vectors are vectors with a magnitude of 1 and are often used to represent directions in vector calculations.
3. Can you provide examples of parallel vectors in real-world scenarios?
Ans. Examples of parallel vectors include the force and weight vectors acting on an object on an inclined plane or the velocity vector of a moving car.
4. What is the significance of position vectors in vector analysis?
Ans. Position vectors are used to represent the location of a point in space relative to a reference point, making them essential in various mathematical and physical applications.
5. How are zero vectors defined and what role do they play in vector algebra?
Ans. Zero vectors have a magnitude of zero and are used as a reference point in vector operations, such as addition and subtraction.
209 videos|443 docs|143 tests
Download as PDF

Up next

Explore Courses for JEE exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

Semester Notes

,

Extra Questions

,

study material

,

Viva Questions

,

Sample Paper

,

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

,

pdf

,

mock tests for examination

,

ppt

,

Objective type Questions

,

past year papers

,

MCQs

,

Important questions

,

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

,

shortcuts and tricks

,

Types of Vectors | Mathematics (Maths) for JEE Main & Advanced

,

Free

,

Summary

,

video lectures

,

Exam

,

Previous Year Questions with Solutions

,

practice quizzes

;