Concept of Vector Addition, Explanation and Important Questions

Using vector addition, two vectors, a and b, can be added together, and a + b will be the resultant vector.

Here are some conditions that are to be followed while adding vectors.

  • Only the same nature of vectors can be added together. For example, acceleration must be added to acceleration and not mass.
  • Vectors and scalars cannot be added.

Consider two vectors C and D. Where, C = Cxi + Cyj + Czk and D = Dxi + Dyj + Dzk. Then, the resultant vector (or vector sum) R = C + D = (Cx + Dx)i + (Cy + Dy)j + (Cz + Cz) k

Read more about vectors and scalars: Vectors and Scalars

Vectors can be divided into vertical and horizontal components. For example, a vector A at an angle Φ, as shown in the below-given image, can be divided into its horizontal and vertical components as:

Using vector addition, two vectors, a and b, can be added together, and a + b will be the resultant vector.

Therefore, vector A can be expressed as:

A = Ax + Ay

Ax = A cos Φ

Ay = A sin Φ

Triangle Law of Addition of Vectors

According to this law, two vectors should be placed so that the head of the first vector links the tail of the second vector, and by placing them this way, both vectors can be added together.

Here are the steps to perform the addition of vectors using the triangle law –

  • Firstly, the two vectors M and N are positioned together so that the head of vector M joins the tail of vector N.
  • And then, a resultant vector S is drawn so that it connects the =of M to the head of N to find the sum.
  • Thus, mathematically, the sum, or the resultant, vector S, in the below-given image can be articulated as S = M + N.
Using vector addition, two vectors, a and b, can be added together, and a + b will be the resultant vector.

Parallelogram Law of Addition of Vectors

Parallelogram law of the addition of vectors is another law for the addition of vectors. Let’s take two vectors, p and q, as shown below.

Using vector addition, two vectors, a and b, can be added together, and a + b will be the resultant vector.

Two adjacent sides of a parallelogram are formed by them in their magnitude and direction. The sum p + q is represented in magnitude and direction by the diagonal of the parallelogram through their mutual point. This is the Parallelogram law of vector addition.

In the above-given figure, using the Triangle law, we can accomplish the following:

OP + PR = OR

OP + OQ = OR, since PR = OQ

Important Questions on Addition of Vectors

1) What is the Vector Addition Rule?

Vector addition rules are the rules to be followed while adding vectors.

  1. Only the same nature of vectors can be added. For example, acceleration must be added with acceleration only and not mass.
  2. Vectors and scalars cannot be added.

2) Is the Addition of Vectors Commutative?

Yes, vector addition is commutative; for any two random vectors c and d,

c + d = d + c.

3) Differentiate between parallelogram law of vector addition and triangle law of vector addition.

For any two given vectors, the parallelogram law of vector addition says that the diagonal becomes the resultant sum vector,. In contrast, for the same condition the triangle law of vector addition says that, the third side of the triangle will become the resultant sum vector.

4) Find the addition of vectors PQ and QR, where PQ = (3, 2) and QR = (2, 6)

We will perform the vector addition by adding their corresponding components

PQ + QR = (3, 4) + (2, 6)

= (3 + 2, 4 + 6) = (5, 10).

5) What is the Formula of Parallelogram Law of Addition of Vectors?

The magnitude of the sum, |a + b|, is given by √(a2+b2+2abcos(θ)) for two given vectors a and b making an angle θ, according to the parallelogram law of addition of vectors.

6) What is the Associative Property of Addition of Vectors?

For any three random vectors a, b, and c, addition is associative (a + b) + c = a + (b + c) i.e., the order of addition does not matter.

7) If a = <1, -1> and b = <2, 1> then find the unit vector in the direction of addition of vectors a and b.

The vector sum will be written as: a + b = <1, -1> + <2, 1> = <1 + 2, -1 + 1> = <3, 0>

Its magnitude will be, |a + b| = √ (32 + 02) = 3.

In the direction of vector addition, the unit vector is: (a + b) / |a + b| = <3, 0> / 3 = <1, 0>. The required unit vector is, <1, 0>.

8) What will be the magnitude of the resulting vector when two vectors in the same direction are added?

When two vectors in the same direction are added to each other, then, the lengths will be added. The resultant vector will bear the resultant length where length is the magnitude of the vector. Hence, the magnitudes add to give the magnitude of the resultant vector.

9) A vector, 6 units from the origin, along the X axis, is added to the vector 12 units from the origin along the Y axis. What is the resultant vector?

The vector 6 units from the origin and along the X axis is 6î. The vector 12 units from the origin and along Y axis is 12ĵ. Hence, the sum is 6î + 12ĵ.

10) Adding 3î + 8ĵ and î + ĵ gives

When 3î + 8ĵ is added to î + ĵ, the corresponding components get added. Hence, the answer is 4î + 9ĵ.

Practice Questions

  1. The vector 45î + 32ĵ is added to a vector. The result gives 15î + 3ĵ as the answer. The unknown vector is:
  2. A vector, 7 units from the origin, along the X axis, is added to vector 3 units along the Y axis. What is the resultant vector?
  3. What is the angle between B and C if three vectors A, B and C have magnitudes 6, 12 and 14 and →A+→B=→CA→+B→=C→ ?
  4. 5N and 12 N are two force vectors and at what angle should they be added to get a resultant vector of 13 N?
  5. What will be the displacement from the initial point, if a person travels 10 km North and 20 km East?

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.

CBSE Unit-wise Class 11 Physics Syllabus

Below we have provided the details of the CBSE Physics topics under each unit as per the revised CBSE Class 11 Physics Syllabus for the 2023-24 academic year. Go through it to get the details of the chapters given below.

Unit-I: Physical World and Measurement

Chapter 2: Units and Measurements

Need for measurement: Units of measurement; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures.

Dimensions of physical quantities, dimensional analysis and its applications.

Unit-II: Kinematics

Chapter 3: Motion in a Straight Line

Frame of reference, Motion in a straight line, Elementary concepts of differentiation and integration for describing motion, uniform and nonuniform motion, and instantaneous velocity, uniformly accelerated motion, velocity-time and position-time graphs. Relations for uniformly accelerated motion (graphical treatment).

Chapter 4: Motion in a Plane

Scalar and vector quantities; position and displacement vectors, general vectors and their notations; equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors, relative velocity, Unit vector; resolution of a vector in a plane, rectangular components, Scalar and Vector product of vectors.

Motion in a plane, cases of uniform velocity and uniform acceleration-projectile motion, uniform circular motion.

Unit-III: Laws of Motion

Chapter 5: Laws of Motion

Intuitive concept of force, Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion (recapitulation only). Law of conservation of linear momentum and its applications. Equilibrium of concurrent forces, Static and kinetic friction, laws of friction, rolling friction, lubrication.

Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road).

Unit-IV: Work, Energy and Power

Chapter 6: Work, Energy and Power

Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.

Notion of potential energy, potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); non-conservative forces: motion in a vertical circle; elastic and inelastic collisions in one and two dimensions.

Unit-V: Motion of System of Particles and Rigid Body

Chapter 7: System of Particles and Rotational Motion

Centre of mass of a two-particle system, momentum conservation and centre of mass motion. Centre of mass of a rigid body; centre of mass of a uniform rod. Moment of a force, torque, angular momentum, law of conservation of angular momentum and its applications.

Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions.

Moment of inertia, radius of gyration, values of moments of inertia for simple geometrical objects (no derivation).

Unit-VI: Gravitation

Chapter 8: Gravitation

Kepler’s laws of planetary motion, universal law of gravitation. Acceleration due to gravity and its variation with altitude and depth. Gravitational potential energy and gravitational potential, escape speed, orbital velocity of a satellite.

Unit-VII: Properties of Bulk Matter

Chapter 9: Mechanical Properties of Solids

Elasticity, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear modulus of rigidity (qualitative idea only), Poisson’s ratio; elastic energy.

Chapter 10: Mechanical Properties of Fluids

Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes), effect of gravity on fluid pressure.

Viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli’s theorem and its applications.

Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise.

Chapter 11: Thermal Properties of Matter

Heat, temperature,( recapitulation only) thermal expansion; thermal expansion of solids, liquids and gases, anomalous expansion of water; specific heat capacity; Cp, Cv – calorimetry; change of state – latent heat capacity.

Heat transfer-conduction, convection and radiation (recapitulation only), thermal conductivity, qualitative ideas of Blackbody radiation, Wein’s displacement Law, Stefan’s law.

Unit-VIII: Thermodynamics

Chapter 12: Thermodynamics

Thermal equilibrium and definition of temperature (zeroth law of thermodynamics), heat, work and internal energy. First law of thermodynamics, Second law of thermodynamics: gaseous state of matter, change of condition of gaseous state -isothermal, adiabatic, reversible, irreversible, and cyclic processes.

Unit-IX: Behaviour of Perfect Gases and Kinetic Theory of Gases

Chapter 13: Kinetic Theory

Equation of state of a perfect gas, work done in compressing a gas.

Kinetic theory of gases – assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro’s number.

Unit-X: Oscillations and Waves

Chapter 14: Oscillations

Periodic motion – time period, frequency, displacement as a function of time, periodic functions and their application.

Simple harmonic motion (S.H.M) and its equations of motion; phase; oscillations of a loaded spring- restoring force and force constant; energy in S.H.M. Kinetic and potential energies; simple pendulum derivation of expression for its time period.

Chapter 15: Waves

Wave motion: Transverse and longitudinal waves, speed of travelling wave, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats.

Students can also access the syllabus for other subjects by visiting Syllabus page of CBSE Class 11.

CBSE Syllabus for Class 11 Physics Practical

Below are the list of the experiments of Physics practicals.

Evaluation Scheme for Class 11 Physics Practical 2023-24

Topic Marks
Two experiments, one from each section7 + 7
Practical record (experiment and activities)5
One activity from any section3
Investigatory Project3
Viva on experiments, activities and project5
Total 30

CBSE Class 11 Physics Practical Syllabus

Section – A

CBSE 11 Physics Syllabus Experiments 

1. To measure the diameter of a small spherical/cylindrical body and to measure internal diameter and depth of a given beaker/calorimeter using Vernier Callipers and hence find its volume.
2. To measure the diameter of a given wire and thickness of a given sheet using screw gauge.
3. To determine the volume of an irregular lamina using the screw gauge.
4. To determine the radius of curvature of a given spherical surface by a spherometer.
5. To determine the mass of two different objects using a beam balance.
6. To find the weight of a given body using parallelogram law of vectors.
7. Using a simple pendulum, plot its L-T2 graph and use it to find the effective length of second’s pendulum.
8. To study variation of time period of a simple pendulum of a given length by taking bobs of same size but different masses and interpret the result.
9. To study the relationship between force of limiting friction and normal reaction and to find the co- efficient of friction between a block and a horizontal surface.
10. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of the earth and study its relationship with the angle of inclination θ by plotting graph between force and sin θ.

CBSE 11 Physics Syllabus Activities

1. To make a paper scale of given least count, e.g., 0.2cm, 0.5 cm.
2. To determine mass of a given body using a metre scale by principle of moments.
3. To plot a graph for a given set of data, with proper choice of scales and error bars.
4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.
5. To study the variation in range of a projectile with angle of projection.
6. To study the conservation of energy of a ball rolling down on an inclined plane (using a double inclined plane).
7. To study dissipation of energy of a simple pendulum by plotting a graph between square of amplitude and time.

Section – B

CBSE 11 Physics Syllabus Experiments 

1. To determine Young’s modulus of elasticity of the material of a given wire.
2. To find the force constant of a helical spring by plotting a graph between load and extension.
3. To study the variation in volume with pressure for a sample of air at constant temperature by plotting graphs between P and V, and between P and 1/V.
4. To determine the surface tension of water by capillary rise method.
5. To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.
6. To study the relationship between the temperature of a hot body and time by plotting a cooling curve.
7. To determine specific heat capacity of a given solid by method of mixtures.
8. To study the relation between frequency and length of a given wire under constant tension using sonometer.
9. To study the relation between the length of a given wire and tension for constant frequency using sonometer.
10. To find the speed of sound in air at room temperature using a resonance tube by two resonance positions.

CBSE 11 Physics Syllabus Activities

1. To observe change of state and plot a cooling curve for molten wax.
2. To observe and explain the effect of heating on a bi-metallic strip.
3. To note the change in level of liquid in a container on heating and interpret the observations.
4. To study the effect of detergent on surface tension of water by observing capillary rise.
5. To study the factors affecting the rate of loss of heat of a liquid.
6. To study the effect of load on depression of a suitably clamped metre scale loaded at (i) its end (ii) in the middle.
7. To observe the decrease in pressure with increase in velocity of a fluid.

Practical Examination for Visually Impaired Students of Class 11 Evaluation Scheme

Time: 2 Hours
Max. Marks: 30

Topic Marks
Identification/Familiarity with the apparatus5
Written test (based on given/prescribed practicals)10
Practical Record5
Viva10
Total30

A. Items for Identification/Familiarity of the apparatus for assessment in practicals (All experiments). 

Spherical ball, Cylindrical objects, vernier calipers, beaker, calorimeter, Screw gauge, wire, Beam balance, spring balance, weight box, gram and milligram weights, forcep, Parallelogram law of vectors apparatus, pulleys and pans used in the same ‘weights’ used, Bob and string used in a simple pendulum, meter scale, split cork, suspension arrangement, stop clock/stop watch, Helical spring, suspension arrangement used, weights, arrangement used for measuring extension, Sonometer, Wedges, pan and pulley used in it, ‘weights’ Tuning Fork, Meter scale, Beam balance, Weight box, gram and
milligram weights, forceps, Resonance Tube, Tuning Fork, Meter scale, Flask/Beaker used for adding water.

B. List of Practicals

1. To measure diameter of a small spherical/cylindrical body using vernier calipers.
2. To measure the internal diameter and depth of a given beaker/calorimeter using vernier calipers and hence find its volume.
3. To measure diameter of given wire using screw gauge.
4. To measure thickness of a given sheet using screw gauge.
5. To determine the mass of a given object using a beam balance.
6. To find the weight of given body using the parallelogram law of vectors.
7. Using a simple pendulum plot L-T and L-T2 graphs. Hence find the effective length of second’s pendulum using appropriate length values.
8. To find the force constant of given helical spring by plotting a graph between load and extension.
9. (i) To study the relation between frequency and length of a given wire under constant tension using a sonometer.
(ii) To study the relation between the length of a given wire and tension, for
constant frequency, using a sonometer.
10. To find the speed of sound in air, at room temperature, using a resonance tube, by observing the two resonance positions.

Note: The above practicals of CBSE 11 Physics Syllabus may be carried out in an experiential manner rather than recording observations.

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Frequently Asked Questions on CBSE Class 11 Physics Syllabus

Q1

According to the CBSE Class 11 Physics Syllabus, which are the units of high marks weightage?

According to the CBSE Class 11 Physics Syllabus, physical world and measurement, kinematics and laws of motion are the units of high-mark weightage.

Q2

How is the practical syllabus of the CBSE Class 11 Physics divided into sections A and B?

The practical syllabus of the CBSE Class 11 Physics contains 10 experiments in section A and 10 experiments in section B with 7 physical activities mentioned for each.

Q3

Which are the basic concepts present in the CBSE Syllabus for Class 11 Physics?

The basic concepts present in the CBSE Syllabus for Class 11 Physics are Thermodynamics, Laws of Motion, Oscillations and Waves.