# Physics Coaching Center In Jalandhar

## Call 9463138669, Anand Classes – JEE Main & Advanced Exam Coaching Center in Jalandhar.

#### JEE & NEET Coaching Center In Jalandhar

#778 Urban Estate Phase-2, Near MGN School Jalandhar City, Punjab 144003

### ANAND CLASSES offers JEE Main & Advanced Exam Coaching Center in Urban Estate Phase-II Jalandhar.

Useful Study Material For the students and teachers to study and teach respectively by clicking from the following links.

## VIDEO LECTURES OF CHAPTER : VECTORS

### CONTENT

1. Scalar and vector quantities
2. Position and displacement vectors
3. general vectors and their notations
4. equality of vectors, multiplication of vectors by a real number
5. addition and subtraction of vectors
6. Relative velocity
7. Unit vector
8. Resolution of a vector in a plane – rectangular components
9. Scalar and Vector product of vectors

## DETAIL THEORY

### CONTENT

1. Scalar and vector quantities
2. Position and displacement vectors
3. general vectors and their notations
4. equality of vectors
5. multiplication of vectors by a real number
6. addition and subtraction of vectors
7. Addition and subtraction of vectors – graphical method
8. Relative velocity
9. Unit vector
10. Resolution of a vector in a plane – rectangular components
11. Scalar and Vector product of vectors
12. VERY SHORT ANSWER TYPE PROBLEMS
13. MCQs
14. Tips & Tricks to solve the problems
15. Synopsis
16. JEE Question Bank

## NCERT BOOK

### Detailed NCERT Syllabus for Class 11 Physics of Chapter Vectors

1.Scalars and Vectors

2.Position and Displacement Vectors

3.Equality of Vectors

4.Negative, Equal, Co-initial, Coplanar, Collinear, Unit and Zero Vectors

5.Multiplication of Vectors by Real Numbers

6.Addition of Vectors – Triangle, Parallelogram and Polygon Laws

7.Commutative and Associative Properties of Vectors

8.Subtraction of Vectors

9.Resolution of Vectors in 2D – Rectangular Components – Graphical

10.Resolution of Vectors in 2D – Rectangular Components – Trigonometry

11.Resolution of Vectors in 2D in terms of Two Given Vectors

12.Resolution of Vectors in 3D – Rectangular Components

13.Vector Addition – Analytical Method (2D & 3D)

14.Magnitude and Direction of the Resultant of Two Vectors A and B, Cosine Rule & Sine Rule

15.Dot Product and Cross Product

SCALARS AND VECTORS

All the physical quantities can be divided into two types.

They are:

(i) Scalars and

(ii) Vectors

The basic difference between them is the ′direction′.

Scalar

A physical quantity which has a magnitude but no direction is called scalar.

Example:  Mass, length, temperature, time, density, work, specific heat, etc.

A scalar may be positive or negative.  Scalars can be added, subtracted, multiplied or divided according to rules of ordinary algebra.

Addition and subtraction of scalars make sense only for quantities of same nature

However, multiplication and division can be performed with different quantities

Vector

A physical quantity which has both magnitude and direction is called vector.

Example: Velocity, acceleration, displacement, force, momentum, torque, etc.

Vectors cannot be added, subtracted, multiplied or divided according to simple rules of algebra.

Vectors can be added, subtracted or multiplied according to the rules of vector algebra.

A vector cannot be divided by another vector as it is not a valid operation in vector algebra.

A vector quantity obeys the ′triangle law of addition′ or equivalently the ′parallelogram law of addition′.

Two vectors A and B are said to be equal if, and only if, they have the same magnitude and the same direction.

The negative of a vector is defined as another vector having the same magnitude but drawn in the opposite direction.

Two vectors A and B are said to be equal if, and only if, they have the same magnitude and the same direction.

Two vectors are said to be co-initial, if they have a common initial point

Two vectors are said to be co-terminal, if they terminate at a common point.

The vectors are said to be co-planar, if they lie in the same plane.

The vectors drawn in this slide are all co-planar vectors.

Two vectors having equal or unequal magnitudes, which either act along the same line or along the parallel lines in the same direction or along the parallel lines in opposite direction are called collinear vectors.

A vector divided by its magnitude is called a unit vector along the direction of the vector.

or

A unit vector is a vector of unit magnitude pointing in a particular direction.

In our study, vectors do not have fixed locations.  So shifting a vector parallel to itself leaves the vector unchanged.  Such vectors are called ′free vectors′.

However, in some physical applications, location of a vector is important.  Such vectors are calledlocalised vectors′.

Multiplying a vector A with a positive number λ gives a vector whose magnitude is changed by the factor λ but the direction is the same as that of A.

Two or more vectors may be added graphically or geometrically by using the following laws of vector addition:

If two vectors can be represented by the two sides of a triangle taken in the same order, then the resultant is represented completely (both in magnitude and direction) by the third side of the triangle taken in the opposite order.

1. Parallelogram Law of Vector Addition

If the two vectors (to be added) can be represented both in magnitude and direction by the two adjacent sides of a parallelogram, then the resultant is represented completely (both in magnitude and direction) by the diagonal of the parallelogram passing through the starting point of the  vectors.

This law is used to obtain the resultant of more than two vectors.

1. Polygon Law of Vector Addition

If a number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, than the resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.

Subtraction of Vectors

Subtraction of vectors can be defined by vector addition of one  vector with the negative vector of the other.

The process of splitting up a vector into two or more components is known as resolution of vector.

RESOLUTION OF VECTORS

The vectors into which a given vector is split are called component vectors.

The component of a vector in a given direction gives the measure of the effect of the vector in that direction.

## Frequently Asked Questions (FAQ) For JEE Exam

### What does ‘Scalar’ quantity mean?

A physical quantity which has a magnitude but no direction is called scalar. Example:  Mass, length, temperature, time, density, work, specific heat, etc. A scalar may be positive or negative.  Scalars can be added, subtracted, multiplied or divided according to rules of ordinary algebra. Addition and subtraction of scalars make sense only for quantities of same nature.  However, multiplication and division can be performed with different quantities.

### What does ‘Vector’ quantity mean?

A physical quantity which has both magnitude and direction is called vector.
Example: Velocity, acceleration, displacement, force, momentum, torque, etc.
Vectors cannot be added, subtracted, multiplied or divided according to simple rules of algebra.
Vectors can be added, subtracted or multiplied according to the rules of vector algebra.
A vector cannot be divided by another vector as it is not a valid operation in vector algebra.

### What are equal vectors ?

Two vectors A and B are said to be equal if, and only if, they have the same magnitude and the same direction.

### What are co-initial vectors ?

Two vectors are said to be co-initial, if they have a common initial point.

### What are co-terminal vectors ?

Two vectors are said to be co-terminal, if they terminate at a common point.

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