• AglaSem
  • Schools
  • Admission
  • Career
  • News
  • Hindi
  • Mock Test
  • Docs
  • ATSE
aglasem
No Result
View All Result
aglasem
  • Home
  • CBSE
    • Date Sheet
    • Syllabus
    • Sample Papers
    • Question Papers
  • ICSE / ISC
  • State Boards
    • Date Sheet
    • Admit Card
    • Result
    • Sample Paper
    • Question Paper
  • NCERT
    • NCERT Solutions
    • NCERT Books
    • NCERT Audio Books
    • NCERT Exempler
  • Study Material
    • Notes
    • Solved Sample Papers
    • Maps
    • Writing Skill Format
  • Olympiads
    • NTSE
    • NMMS
  • School Admission
  • Entrance Exams
    • JEE Main
    • NEET
    • CLAT
  • Students Guide
    • Careers Opportunities
    • Courses & Career
    • Courses after 12th
  • Mock Tests
  • Others
    • RD Sharma Solutions
    • HC Verma Solutions
    • Teaching Material
    • Classes Wise Resources
No Result
View All Result
aglasem
No Result
View All Result

CBSE Notes Class 11 Physics Vectors

by aglasem
March 14, 2023
in 11th Class

Class 11 Physics Vectors – Get here the Notes for Class 11 Physics Vectors. Candidates who are ambitious to qualify the Class 11 with good score can check this article for Notes. This is possible only when you have the best CBSE Class 11 Physics study material and a smart preparation plan. To assist you with that, we are here with notes. Hope these notes will helps you understand the important topics and remember the key points for exam point of view. Below we provided the Notes of Class 11 Physics for topic Vectors.

  • Class: 11th
  • Subject: Physics
  • Topic: Vectors
  • Resource: Notes

CBSE Notes Class 11 Physics Vectors

Candidates who are pursuing in Class 11 are advised to revise the notes from this post. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for Class 11 Physics Vectors from this article.

Those physical quantities which require magnitude as well as direction for their complete representation and follows vector laws are called vectors.

Vector can be divided into two types

1. Polar Vectors

These are those vectors which have a starting point or a point of application as a displacement, force etc.

2. Axial Vectors

These are those vectors which represent rotational effect and act along the axis of rotation in accordance with right hand screw rule as angular velocity, torque, angular momentum etc.

Scalars

Those physical quantities which require only magnitude but no direction for their complete representation, are called scalars.

Distance, speed, work, mass, density, etc are the examples of scalars. Scalars can be added, subtracted, multiplied or divided by simple algebraic laws.

Tensors

Tensors are those physical quantities which have different values in different directions at the same point.

Moment of inertia, radius of gyration, modulus of elasticity, pressure, stress, conductivity, resistivity, refractive index, wave velocity and density, etc are the examples of tensors. Magnitude of tensor is not unique.

Different Types of Vectors

(i) Equal Vectors Two vectors of equal magnitude, in same direction are called equal vectors.

CBSE Class 11 Physics Notes Vectors

(ii) Negative Vectors Two vectors of equal magnitude but in opposite directions are called negative vectors.

CBSE Class 11 Physics Notes Vectors

(iii) Zero Vector or Null Vector A vector whose magnitude is zero is known as a zero or null vector. Its direction is not defined. It is denoted by 0.

Velocity of a stationary object, acceleration of an object moving with uniform velocity and resultant of two equal and opposite vectors are the examples of null vector.

(iv) Unit Vector A vector having unit magnitude is called a unit vector.

A unit vector in the direction of vector A is given by

 = A / A

A unit vector is unitless and dimensionless vector and represents direction only.

CBSE Class 11 Physics Notes Vectors

(v) Orthogonal Unit Vectors The unit vectors along the direction of orthogonal axis, i.e., X – axis, Y – axis and Z – axis are called orthogonal unit vectors. They are represented by

CBSE Class 11 Physics Notes Vectors

(vi) Co-initial Vectors Vectors having a common initial point, are called co-initial vectors.

CBSE Class 11 Physics Notes Vectors

(vii) Collinear Vectors Vectors having equal or unequal magnitudes but acting along the same or Ab parallel lines are called collinear vectors.

CBSE Class 11 Physics Notes Vectors

(viii) Coplanar Vectors Vectors acting in the same plane are called coplanar vectors.

(ix) Localised Vector A vector whose initial point is fixed, is called a localised vector.

(x) Non-localised or Free Vector A vector whose initial point is not fixed is called a non-localised or a free vector.

(xi) Position Vector A vector representing the straight line distance and the direction of any point or object with respect to the origin, is called position vector.

Addition of Vectors

1. Triangle Law of Vectors

If two vectors acting at a point are represented in magnitude and direction by the two sides of a triangle taken in one order, then their resultant is represented by the third side of the triangle taken in the opposite order.

If two vectors A and B acting at a point are inclined at an angle θ, then their resultant

R = √A2 + B2 + 2AB cos θ

CBSE Class 11 Physics Notes Vectors

If the resultant vector R subtends an angle β with vector A, then

tan β = B sin θ / A + B cos θ

2. Parallelogram Law of Vectors

If two vectors acting at a point are represented in magnitude and direction by the two adjacent sides of a parallelogram draw from a point, then their resultant is represented in magnitude and direction by the diagonal of the parallelogram draw from the same point.

CBSE Class 11 Physics Notes Vectors

Resultant of vectors A and B is given by

√A2 + B2 + 2AB cos θ

If the resultant vector R subtends an angle β with vector A, then

tan β = B sin θ / A + B cos θ

Polygon Law of Vectors

It states that if number of vectors acting on a particle at a time are represented in magnitude and – direction by the various sides of an open polygon taken in same order, their resultant vector E is represented in magnitude and direction by the closing side of polygon taken in opposite order. In fact, polygon law of vectors is the outcome of triangle law of vectors.

R = A + B + C + D + E

OE = OA + AB + BC + CD + DE

CBSE Class 11 Physics Notes Vectors

Properties of Vector Addition

(i) Vector addition is commutative, i.e., A + B = B + A

(ii) Vector addition is associative, i.e.,

A +(B + C)= B + (C + A)= C + (A + B)

(iii) Vector addition is distributive, i.e., m (A + B) = m A + m B

Rotation of a Vector

(i) If a vector is rotated through an angle 0, which is not an integral multiple of 2 π, the vector changes.

(ii) If the frame of reference is rotated or translated, the given vector does not change. The components of the vector may, however, change.

Resolution of a Vector into Rectangular Components

If any vector A subtends an angle θ with x-axis, then its

Horizontal component Ax = A cos θ

Vertical component Ay = A sin θ

Magnitude of vector A = √Ax2 + Ay2

tan θ = Ay / Ax

CBSE Class 11 Physics Notes Vectors

Direction Cosines of a Vector

If any vector A subtend angles α, β and γ with x – axis, y – axis and z – axis respectively and its components along these axes are Ax, Ay and Az, then

cos α= Ax / A, cos β = Ay / A, cos γ = Az / A

and cos2 α + cos2 β + cos2 γ = 1

Subtraction of Vectors

Subtraction of a vector B from a vector A is defined as the addition of vector -B (negative of vector B) to vector A

Thus, A – B = A + (-B)

Multiplication of a Vector

1. By a Real Number

When a vector A is multiplied by a real number n, then its magnitude becomes n times but direction and unit remains unchanged.

2. By a Scalar

When a vector A is multiplied by a scalar S, then its magnitude becomes S times, and unit is the product of units of A and S but direction remains same as that of vector A.

Scalar or Dot Product of Two Vectors

The scalar product of two vectors is equal to the product of their magnitudes and the cosine of the smaller angle between them. It is denoted by . (dot).

A * B = AB cos θ

CBSE Class 11 Physics Notes Vectors

The scalar or dot product of two vectors is a scalar.

Properties of Scalar Product

(i) Scalar product is commutative, i.e., A * B= B * A

(ii) Scalar product is distributive, i.e., A * (B + C) = A * B + A * C

(iii) Scalar product of two perpendicular vectors is zero.

A * B = AB cos 90° = O

(iv) Scalar product of two parallel vectors is equal to the product of their magnitudes, i.e., A * B = AB cos 0° = AB

(v) Scalar product of a vector with itself is equal to the square of its magnitude, i.e.,

A * A = AA cos 0° = A2

(vi) Scalar product of orthogonal unit vectors

CBSE Class 11 Physics Notes Vectors

CBSE Class 11 Physics Notes Vectors

and

(vii) Scalar product in cartesian coordinates

CBSE Class 11 Physics Notes Vectors

= AxBx + AyBy + AzBz

Vector or Cross Product of Two Vectors

The vector product of two vectors is equal to the product of their magnitudes and the sine of the smaller angle between them. It is denoted by * (cross).

CBSE Class 11 Physics Notes Vectors

A * B = AB sin θ n

The direction of unit vector n can be obtained from right hand thumb rule.

If fingers of right hand are curled from A to B through smaller angle between them, then thumb will represent the direction of vector (A * B).

The vector or cross product of two vectors is also a vector.

Properties of Vector Product

(i) Vector product is not commutative, i.e.,

A * B ≠ B * A  [∴ (A * B) = — (B * A)]

(ii) Vector product is distributive, i.e.,

A * (B + C) = A * B + A * C

(iii) Vector product of two parallel vectors is zero, i.e.,

A * B = AB sin O° = 0

(iv) Vector product of any vector with itself is zero.

A * A = AA sin O° = 0

(v) Vector product of orthogonal unit vectors

CBSE Class 11 Physics Notes Vectors

(vi) Vector product in cartesian coordinates

CBSE Class 11 Physics Notes Vectors

Direction of Vector Cross Product

When C = A * B, the direction of C is at right angles to the plane containing the vectors A and B. The direction is determined by the right hand screw rule and right hand thumb rule.

CBSE Class 11 Physics Notes Vectors

(i) Right Hand Screw Rule Rotate a right handed screw from first vector (A) towards second vector (B). The direction in which the right handed screw moves gives the direction of vector (C).

(ii) Right Hand Thumb Rule Curl the fingers of your right hand from A to B. Then, the direction of the erect thumb will point in the direction of A * B.

Class 11 Key Points, Important Questions & Practice Papers

Hope these notes helped you in your schools exam preparation. Candidates can also check out the Key Points, Important Questions & Practice Papers for various Subjects for Class 11 in both Hindi and English language form the link below.

Class 11 Physics कक्षा 11 अर्थशास्त्र
Class 11 Chemistry कक्षा 11 समाज शास्त्र
Class 11 Maths कक्षा 11 शारीरिक शिक्षा
Class 11 Biology कक्षा 11 राजनीति विज्ञान
Class 11 Business Studies कक्षा 11 इतिहास
Class 11 Accountancy कक्षा 11 भूगोल 
Class 11 Sociology 
Class 11 Physical Education 
Class 11 English 

 Class 11 NCERT Solutions

Candidates who are studying in Class 11 can also check Class 11 NCERT Solutions from here. This will help the candidates to know the solutions for all subjects covered in Class 11th. Candidates can click on the subject wise link to get the same. Class 11 Chapter-wise, detailed solutions to the questions of the NCERT textbooks are provided with the objective of helping students compare their answers with the sample answers.

  • Biology
  • Chemistry
  • Physics
  • Mathematics
  • English
  • Hindi
  • Business Studies

Class 11 Mock Test / Practice

Mock test are the practice test or you can say the blue print of the main exam. Before appearing in the main examination, candidates must try mock test as it helps the students learn from their mistakes. With the help of Class 11 Mock Test / Practice, candidates can also get an idea about the pattern and marking scheme of that examination. For the sake of the candidates we are providing Class 11 Mock Test / Practice links below.

  • Maths
  • Physics
  • Chemistry
  • Biology

 Class 11 Exemplar Questions

Exemplar Questions Class 11 is a very important resource for students preparing for the Examination. Here we have provided Exemplar Problems Solutions along with NCERT Exemplar Problems Class 11. Question from very important topics is covered by Exemplar Questions for Class 11.

Physics रसायन विज्ञान
Chemistry जीव विज्ञान
Maths
Biology

CBSE Notes for Class 11 Physics Notes Biology Notes Maths Notes Chemistry Notes

Tags: CBSE Class 11 NotesClass 11 NotesClass 11thNotesPhysics Notes
Previous Post

CBSE Notes Class 11 Physics Projectile Motion and Circular Motion

Next Post

CBSE Notes Class 11 Biology Transport in Plants

Related Posts

11th Class

Tamil Nadu 11th Model Question Paper 2023 (PDF) – DGE TN Sample Paper for Class 11

11th Class

Tamil Nadu 11th Commerce Model Question Paper 2023 (PDF)

11th Class

Tamil Nadu 11th Accountancy Model Question Paper 2023 (PDF)

11th Class

Tamil Nadu 11th Biology Model Question Paper 2023 (PDF)

Leave a Reply Cancel reply

CBSE Board Quick Links

  • CBSE Date Sheet
  • CBSE Result
  • CBSE Syllabus
  • CBSE Sample Papers
  • CBSE Question Papers
  • CBSE Notes
  • CBSE Practice Papers
  • CBSE Mock Tests

Class Wise Study Material

  • Class 1
  • Class 2
  • Class 3
  • Class 4
  • Class 5
  • Class 6
  • Class 7
  • Class 8
  • Class 9
  • Class 10
  • Class 11
  • Class 12

Board Exams 2023

  • Solved Sample Papers
  • Maps
  • Revision Notes
  • CBSE
  • State Board

Study Material

  • Class Notes
  • NCERT Solutions
  • NCERT Books
  • HC Verma Solutions
  • Courses After Class 12th

Exam Zone

  • JEE Main 2023
  • NEET 2023
  • CLAT 2023
  • Fashion & Design
  • Latest
  • Disclaimer
  • Terms of Use
  • Privacy Policy
  • Contact

© 2019 aglasem.com

  • Home
  • CBSE
    • Date Sheet
    • Syllabus
    • Sample Papers
    • Question Papers
  • ICSE / ISC
  • State Boards
    • Date Sheet
    • Admit Card
    • Result
    • Sample Paper
    • Question Paper
  • NCERT
    • NCERT Solutions
    • NCERT Books
    • NCERT Audio Books
    • NCERT Exempler
  • Study Material
    • Notes
    • Solved Sample Papers
    • Maps
    • Writing Skill Format
  • Olympiads
    • NTSE
    • NMMS
  • School Admission
  • Entrance Exams
    • JEE Main
    • NEET
    • CLAT
  • Students Guide
    • Careers Opportunities
    • Courses & Career
    • Courses after 12th
  • Mock Tests
  • Others
    • RD Sharma Solutions
    • HC Verma Solutions
    • Teaching Material
    • Classes Wise Resources

© 2019 aglasem.com

Play Quiz = Earn Coins Click Here!