CBSE Class 11 Physics Vectors Notes, MCQs, Questions & Answers | NEET Preparation

 - Dr.Sanjaykumar Pawar  

Vectors Class 11 Physics Notes, MCQs, Assertion Reason, Case Study & CBSE Questions

Complete Class 11 Physics Vectors Notes with formulas, diagrams, MCQs, assertion-reason, case studies and CBSE exam questions.

Internal Links

• Class 11 Physics Units and Measurements
• Motion in a Straight Line Notes
• Motion in a Plane
• Projectile Motion
• Laws of Motion
• Work, Energy and Power
• System of Particles
• Circular Motion
• Kinematics Formula Sheet
• Physics Formula Handbook
• NEET Physics Notes
• CBSE Class 11 Physics MCQs
• Class 11 Physics Previous Year Questions
• Class 11 Physics Sample Papers
• NCERT Solutions for Class 11 Physics
• Important Physics Derivations
• Physics Practical Experiments
• Physics Revision Notes
• Physics Chapter-wise Question Bank
• CBSE Class 11 Study Material

NEET Physics Chapter : Vectors

Vectors are one of the most important topics in NEET Physics. Almost every chapter uses vectors. Therefore understanding vectors properly makes Mechanics very easy.

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1. Equality of Vectors

Two vectors are called equal if

• Magnitude is same.
• Direction is same.

Position does NOT matter. Even if vectors are shifted parallel, they are still equal.

Equal vectors ⇒ Same Magnitude + Same Direction

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2. Addition of Vectors

Vector addition means combining two vectors to get one resultant vector.

Triangle Law

Place the tail of second vector at the head of first vector. Join the starting point to the final point. That gives resultant.

Remember: Head to Tail Rule

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3. Parallelogram Law

If two vectors start from the same point, complete a parallelogram. Diagonal gives resultant vector.

Resultant = Diagonal of Parallelogram

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4. Magnitude of Resultant

Suppose

First Vector = a

Second Vector = b

Angle between them = θ

R = √(a² + b² + 2ab cosθ)

This is one of the MOST IMPORTANT formulas for NEET. Learn it perfectly.

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5. Direction of Resultant

tanα = (b sinθ)/(a + b cosθ)

α = angle made by resultant with first vector.

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6. Special Cases

Angle	Magnitude
0°	a+b
180°	|a-b|
90°	√(a²+b²)

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7. Example

Question: Two vectors have equal magnitude A. Angle between them is θ. Find resultant.

Solution

R = √(A²+A²+2A²cosθ)

= √(2A²(1+cosθ))

Using 1+cosθ=2cos²(θ/2)

R = 2A cos(θ/2)

Resultant = 2A cos(θ/2)

Direction:

α = θ/2

The resultant bisects the angle between two equal vectors.

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8. Memory Tricks

✔ Triangle Rule → Head to Tail

✔ Parallelogram Rule → Diagonal

✔ Equal Vectors → Same Magnitude + Same Direction

✔ 90° → Pythagoras

✔ 180° → Subtraction

✔ 0° → Addition

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9. NEET Important Points

• Magnitude is always positive.
• Direction decides vector.
• Vectors obey triangle law.
• Resultant depends on angle.
• Equal vectors can have different positions.
• Parallelogram law is frequently asked in NEET.

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10. Practice Questions

1. Define equal vectors.
2. State triangle law.
3. State parallelogram law.
4. Write magnitude formula.
5. Write direction formula.
6. Find resultant when angle is 90°.
7. Find resultant when angle is 180°.
8. Two vectors 10 N each make 60°. Find resultant.
9. Two vectors 5 N each make 120°. Find resultant.
10. Why does the resultant bisect equal vectors?

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Summary

• Equal vectors → Same magnitude + same direction
• Triangle Law → Head to Tail
• Parallelogram Law → Diagonal
• Magnitude → √(a²+b²+2abcosθ)
• Direction → tanα=(bsinθ)/(a+bcosθ)
• Equal vectors → Resultant = 2Acos(θ/2)
• Direction = θ/2

CBSE Class 11 Physics

Chapter : Vectors Question Bank

1. Multiple Choice Questions (MCQs)

1. A vector quantity has

1. Only magnitude
2. Only direction
3. Magnitude and direction
4. None

Answer: C

2. Equal vectors have

1. Equal magnitude only
2. Equal direction only
3. Equal magnitude and direction
4. Different directions

Answer: C

3. The diagonal of a parallelogram represents

1. Difference of vectors
2. Resultant vector
3. Unit vector
4. Zero vector

Answer: B

2. Very Short Answer Questions (1 Mark)

Q1. Define a vector.

A quantity having both magnitude and direction is called a vector.

Q2. Give one example of a vector.

Velocity.

Q3. What is a zero vector?

A vector whose magnitude is zero.

3. Short Answer Questions (2-3 Marks)

Q1. Define equal vectors.

Two vectors having equal magnitude and same direction are called equal vectors.

Q2. State the triangle law of vector addition.

If two vectors are represented by two sides of a triangle taken in order, the third side taken in opposite order represents the resultant.

4. Long Answer Questions (5 Marks)

Q1. Explain the parallelogram law of vector addition with diagram.

If two vectors acting simultaneously are represented by two adjacent sides of a parallelogram, then the diagonal passing through the common point represents the resultant vector. Magnitude: R = √(A² + B² + 2AB cosθ) Direction: tanα = (B sinθ)/(A + B cosθ)

5. Assertion and Reason

Assertion: Equal vectors may have different positions.

Reason: A vector depends only on magnitude and direction.

Answer: Both Assertion and Reason are true, and Reason correctly explains Assertion.

Assertion: Scalar quantities have direction.

Reason: Scalars possess only magnitude.

Answer: Assertion is false. Reason is true.

6. Fill in the Blanks

Question	Answer
A vector has ______ and ______.	Magnitude, Direction
The diagonal of a parallelogram gives the ______.	Resultant
A quantity having only magnitude is called ______.	Scalar
The SI unit of displacement is ______.	metre

7. Match the Columns

Column A	Column B
Velocity	Vector
Mass	Scalar
Acceleration	Vector
Time	Scalar

Answers Velocity → Vector Mass → Scalar Acceleration → Vector Time → Scalar

8. Statement Based Questions

Statement I: The resultant of two equal vectors bisects the angle between them.

Statement II: The magnitudes of both vectors are equal.

Both statements are true. Statement II explains Statement I.

9. Case Study Questions

Rahul pushes a box with force 20 N towards east. Aman pushes the same box with force 20 N making an angle of 60°. Answer the following.

1. Which law is used?
2. Write the magnitude formula.
3. If angle becomes 180°, what happens?

1. Parallelogram law.
2. R = √(A²+B²+2ABcosθ)
3. Resultant = |A−B|

10. Numerical Questions

Two vectors of magnitude 5 N each make an angle of 60°. Find the resultant.

R = √(25+25+50×0.5) = √75 = 8.66 N

11. HOTS Questions

Why can two vectors be equal even if they are drawn at different places?

Because a vector depends only on magnitude and direction, not on position.

12. Competency Based Questions

A boat is moving across a river. Which physical quantities should be treated as vectors?

Velocity, displacement and acceleration.

13. One Word Questions

Question	Answer
Quantity having direction	Vector
Quantity having only magnitude	Scalar
Magnitude zero vector	Zero Vector
Vector of magnitude one	Unit Vector

14. Important CBSE Questions

1. Define vector.
2. State triangle law.
3. State parallelogram law.
4. Define equal vectors.
5. What is a unit vector?
6. What is a null vector?
7. Derive the magnitude formula.
8. Derive the direction formula.
9. Differentiate scalar and vector.
10. Give five examples each of scalars and vectors.

Retardation (Negative Acceleration) Practice Questions with Answers | CBSE Class 9 & NEET Physics Notes

 Dr Sanjay Kumar Pawar

Retardation (Negative Acceleration) Notes, MCQs & Numericals | CBSE & NEET 

Retardation (Negative Acceleration) explained with formulas, solved examples, and practice questions for CBSE Class 9 and NEET.

Internal Links

1. Motion in One Dimension Notes

2. Distance and Displacement Explained

3. Speed, Velocity and Acceleration Notes

4. Uniform and Non-Uniform Motion

5. Equations of Motion with Derivations

6. Graphs of Motion (Distance-Time & Velocity-Time)

7. Newton's Laws of Motion

8. Force and Inertia Notes

9. Work, Energy and Power

10. Gravitation Notes

11. Units and Measurements

12. Scalars and Vectors

13. Physics Formula Sheet for Class 9

14. CBSE Class 9 Science Chapter-wise Notes

15. NEET Foundation Physics Practice Questions

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Retardation (Negative Acceleration)

CBSE | NCERT | NEET Foundation

Very Short Answer Questions (1 Mark)

1. What is retardation?
   Retardation is the decrease in velocity of a moving body with time. It is also called negative acceleration.
2. What is another name for negative acceleration?
   Deceleration or Retardation.
3. What is the SI unit of retardation?
   m/s²
4. Can acceleration be negative?
   Yes. Negative acceleration is called retardation.
5. A vehicle slows down. What is the sign of acceleration?
   Negative (−)
6. What is the final velocity of a body that comes to rest?
   0 m/s
7. Which equation of motion is used when time is not given?
   v² = u² + 2as
8. What happens to the speed during retardation?
   The speed decreases.
9. What is the SI unit of velocity?
   m/s
10. What is the SI unit of displacement?
    metre (m)

Short Answer Questions (2 Marks)

Q1. Differentiate between Acceleration and Retardation

Acceleration	Retardation
Speed increases	Speed decreases
Positive	Negative
Velocity increases	Velocity decreases

Q2. Write the three equations of motion.

v = u + at

s = ut + ½at²

v² = u² + 2as

Q3. Write the equations for retardation.

v = u − at

s = ut − ½at²

v² = u² − 2as

Solved Numerical Questions (3 Marks)

Question 1

A bike moves with an initial velocity of 20 m/s. It stops after 5 seconds. Find its retardation.

Given
u = 20 m/s
v = 0 m/s
t = 5 s

v = u + at

0 = 20 + 5a

5a = -20

a = -4 m/s²

Retardation = 4 m/s²

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Question 2

A car moving at 30 m/s comes to rest in 6 seconds. Find the retardation.

Given
u = 30 m/s
v = 0 m/s
t = 6 s

v = u + at

0 = 30 + 6a

6a = -30

a = -5 m/s²

Retardation = 5 m/s²

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Question 3

A train slows down from 40 m/s to 20 m/s in 10 seconds. Find the acceleration.

Given
u = 40 m/s
v = 20 m/s
t = 10 s

v = u + at

20 = 40 + 10a

10a = -20

a = -2 m/s²

Retardation = 2 m/s²

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Question 4

A bus moving at 25 m/s stops after travelling 125 m. Find the retardation.

Given
u = 25 m/s
v = 0 m/s
s = 125 m

v² = u² + 2as

0 = 25² + 2 × a × 125

0 = 625 + 250a

250a = -625

a = -2.5 m/s²

Retardation = 2.5 m/s²

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Question 5

A car moving at 15 m/s stops after travelling 45 m. Find the retardation.

Given
u = 15 m/s
v = 0 m/s
s = 45 m

v² = u² + 2as

0 = 15² + 2 × a × 45

0 = 225 + 90a

90a = -225

a = -2.5 m/s²

Retardation = 2.5 m/s²

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Question 6

A scooter slows from 18 m/s to 6 m/s in 4 seconds. Find the retardation.

a = (6 − 18) / 4

a = -3 m/s²

Retardation = 3 m/s²

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Question 7

A train moving at 72 m/s stops in 12 seconds. Find the retardation.

a = (0 − 72) / 12

a = -6 m/s²

Retardation = 6 m/s²

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Question 8

A bus slows from 50 m/s to 20 m/s in 10 seconds. Find the retardation.

a = (20 − 50) / 10

a = -3 m/s²

Retardation = 3 m/s²

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Question 9

A car moving at 10 m/s stops in 2 seconds. Find the retardation.

a = (0 − 10) / 2

a = -5 m/s²

Retardation = 5 m/s²

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Question 10

A truck moving at 36 m/s comes to rest in 9 seconds. Find the retardation.

a = (0 − 36) / 9

a = -4 m/s²

Retardation = 4 m/s²

Multiple Choice Questions (MCQs)

1. Retardation is also called

A. Positive Acceleration
B. Uniform Motion
C. Negative Acceleration
D. Velocity

Answer: C. Negative Acceleration

2. SI unit of acceleration is

A. metre
B. second
C. m/s²
D. km/h

Answer: C. m/s²

3. When brakes are applied, acceleration becomes

A. Positive
B. Zero
C. Negative
D. Infinite

Answer: C. Negative

4. Which equation is used when time is not given?

A. v = u + at
B. s = ut
C. v² = u² + 2as
D. a = v/t

Answer: C. v² = u² + 2as

5. Final velocity of a body at rest is

A. 5 m/s
B. 10 m/s
C. 0 m/s
D. 100 m/s

Answer: C. 0 m/s

6. Retardation decreases

A. Time
B. Velocity
C. Distance
D. Mass

Answer: B. Velocity

7. Initial velocity is represented by

A. v
B. s
C. u
D. t

Answer: C. u

8. Final velocity is represented by

A. u
B. a
C. s
D. v

Answer: D. v

9. Time is represented by

A. a
B. t
C. s
D. u

Answer: B. t

10. Displacement is represented by

A. s
B. a
C. u
D. v

Answer: A. s

Higher Order Thinking Questions (HOTS)

Q1. Why is retardation called negative acceleration?

Retardation acts opposite to the direction of motion and decreases the velocity of a moving body. Therefore, its value is negative.

Q2. Can a body move forward while having negative acceleration?

Yes. If a moving body slows down while still moving forward, it has negative acceleration (retardation).

Assertion and Reason

Question 1

Assertion (A): Retardation decreases the speed of a moving body.

Reason (R): Retardation acts opposite to the direction of motion.

Both Assertion and Reason are true, and Reason is the correct explanation of Assertion.

Question 2

Assertion (A): A car moving at constant speed has retardation.

Reason (R): Constant speed means acceleration is zero.

Assertion is false, but Reason is true.

Case Study Question

A car is moving with an initial velocity of 60 m/s. The driver applies brakes and the car stops after travelling 180 m.

Questions

1. What is the initial velocity?
2. What is the final velocity?
3. Which equation of motion will be used?
4. Find the retardation.

Answers

Initial Velocity = 60 m/s

Final Velocity = 0 m/s

Formula Used:

v² = u² + 2as

0 = 60² + 2 × a × 180

0 = 3600 + 360a

360a = -3600

a = -10 m/s²

Retardation = 10 m/s²

Quick Revision

v = u + at

s = ut + ½at²

v² = u² + 2as

For Retardation

v = u − at

s = ut − ½at²

v² = u² − 2as

Exam Tips

• Always write the SI unit in the final answer.
• Write: Given → Formula → Substitution → Calculation → Final Answer.
• Use v² = u² + 2as when time is not given.
• Negative acceleration means retardation.
• If the body stops, final velocity (v) = 0.

CBSE & NEET Foundation Physics Notes

Practice Daily • Revise Formulas • Solve Numericals • Score Full Marks

Resolution of Vectors Class 11 Physics Notes, MCQs & Examples (NEET + CBSE)

 RESOLUTION OF VECTORS

│

├── 1. Meaning

│   ├── Splitting a vector into components

│   ├── Components add to form original vector

│   └── Used in force, motion, displacement problems

│

├── 2. Vector Resolution in Plane

│   ├── Vector A resolved along vectors a and b

│   ├── Formula:

│   │      A = λa + μb

│   ├── λ and μ are real numbers

│   └── Component vectors:

│          ├── λa

│          └── μb

│

├── 3. Unit Vectors

│   ├── Magnitude = 1

│   ├── Show direction only

│   ├── No dimension or unit

│   ├── Along axes:

│   │      ├── î → x-axis

│   │      ├── ĵ → y-axis

│   │      └── k̂ → z-axis

│   └── Properties:

│          ├── |î| = |ĵ| = |k̂| = 1

│          └── Mutually perpendicular

│

├── 4. Vector in Unit Vector Form

│   ├── Formula:

│   │      A = |A| n̂

│   ├── |A| → magnitude

│   └── n̂ → unit vector along A

│

├── 5. Resolution Along x and y Axes

│   ├── Vector A in x-y plane

│   ├── Components:

│   │      ├── Ax along x-axis

│   │      └── Ay along y-axis

│   └── Vector form:

│          A = Ax î + Ay ĵ

│

├── 6. Component Formulae

│   ├── Ax = A cosθ

│   ├── Ay = A sinθ

│   └── θ = angle with x-axis

│

├── 7. Nature of Components

│   ├── Positive

│   ├── Negative

│   └── Zero

│

├── 8. Magnitude of Vector

│   └── Formula:

│          A = √(Ax² + Ay²)

│

├── 9. Direction of Vector

│   ├── tanθ = Ay/Ax

│   └── θ = tan⁻¹(Ay/Ax)

│

├── 10. Ways to Represent Vector

│   ├── By magnitude and direction

│   │      ├── A

│   │      └── θ

│   └── By components

│          ├── Ax

│          └── Ay

│

├── 11. Resolution in 3D

│   ├── Components:

│   │      ├── Ax = A cosα

│   │      ├── Ay = A cosβ

│   │      └── Az = A cosγ

│   ├── Vector form:

│   │      A = Ax î + Ay ĵ + Az k̂

│   └── Magnitude:

│          A = √(Ax² + Ay² + Az²)

│

├── 12. Position Vector

│   └── r = xî + yĵ + zk̂

│

├── 13. NEET Important Points

│   ├── x-component → cosine

│   ├── y-component → sine

│   ├── Components are scalars

│   └── Axî and Ayĵ are vectors

│

└── 14. Common Mistakes

    ├── Wrong sign of components

    ├── Confusing sin and cos

    ├── Ignoring quadrant

    └── Treating Ax as vector

Resolution of a vector into x and y components showing Ax = A cosθ and Ay = A sinθ on Cartesian axes.

 

- Dr.Sanjaykumar pawar

Internal Links 

/class-11-physics-vectors

/motion-in-a-plane-notes

/neet-physics-important-formulas

/physics-mcqs-class-11

/unit-vectors-and-components

/cbse-class-11-physics-notes

/physics-numericals-practice-set

Resolution of Vectors – NEET Notes

1. Meaning of Resolution of Vectors

Resolution of a vector means splitting a vector into two or more parts called components.

These components combine together to form the original vector.

Example: A diagonal force can be divided into horizontal and vertical components.

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2. Resolving a Vector in a Plane

Let there be two vectors a and b in the same plane. Another vector A can be written as:

A = λa + μb

Where:

• λ and μ are real numbers
• λa and μb are component vectors

Vector A is said to be resolved into components along vectors a and b.

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3. Unit Vectors

A unit vector is a vector having magnitude equal to 1.

It is used only to represent direction.

Unit Vectors Along Coordinate Axes

• Along x-axis → î
• Along y-axis → ĵ
• Along z-axis → k̂

|î| = |ĵ| = |k̂| = 1

Unit vectors have no dimensions and no units.

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4. Vector in Terms of Unit Vector

Any vector can be written as:

A = |A| n̂

Where:

• |A| = magnitude of vector
• n̂ = unit vector in direction of A

---

5. Resolution Along x and y Axes

A vector A in a plane can be resolved into x-component and y-component.

A = Ax î + Ay ĵ

Where:

• Ax = x-component
• Ay = y-component

---

6. Formula for Components

If vector A makes angle θ with x-axis:

Ax = A cosθ

Ay = A sinθ

x-component uses cosine and y-component uses sine.

---

7. Sign of Components

Components can be positive, negative, or zero depending on direction.

Quadrant	x-component	y-component
First	Positive	Positive
Second	Negative	Positive
Third	Negative	Negative
Fourth	Positive	Negative

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8. Magnitude of Vector

If Ax and Ay are known:

A = √(Ax² + Ay²)

This formula is based on Pythagoras theorem.

---

9. Direction of Vector

tanθ = Ay / Ax

Therefore:

θ = tan⁻¹(Ay / Ax)

---

10. Two Ways to Represent a Vector

Method 1

• Magnitude A
• Direction θ

Method 2

• x-component Ax
• y-component Ay

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11. Resolution in Three Dimensions

In 3D, a vector has three components:

Ax = A cosα

Ay = A cosβ

Az = A cosγ

Where:

• α = angle with x-axis
• β = angle with y-axis
• γ = angle with z-axis

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12. Vector Form in 3D

A = Ax î + Ay ĵ + Az k̂

---

13. Magnitude in 3D

A = √(Ax² + Ay² + Az²)

---

14. Position Vector

A position vector is written as:

r = x î + y ĵ + z k̂

Where x, y, z are coordinates of the point.

---

15. NEET Important Points

• Resolution means splitting vectors into components.
• Unit vectors show direction only.
• î, ĵ, k̂ are unit vectors.
• Ax = A cosθ
• Ay = A sinθ
• A = √(Ax² + Ay²)
• tanθ = Ay / Ax

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16. Common NEET Mistakes

• Forgetting signs of components
• Confusing sine and cosine
• Ignoring quadrant rules
• Writing scalar as vector

---

17. Quick Trick for NEET

• Cos → adjacent side
• Sin → opposite side
• x-component → cosine
• y-component → sine

Prepared for NEET Physics Students

Class 11 Physics - Resolution of Vectors

1. Multiple Choice Questions (MCQs)

Q1. Resolution of a vector means:

(a) Adding vectors
(b) Splitting into components
(c) Multiplying vectors
(d) Rotating vectors

Answer: (b) Splitting into components

Q2. Unit vector has magnitude:

(a) 0 (b) 1 (c) 2 (d) infinite

Answer: (b) 1

Q3. x-component of vector A is:

(a) A sinθ (b) A cosθ (c) A tanθ (d) A cotθ

Answer: (b) A cosθ

Q4. Unit vector along x-axis is:

Answer: î

2. Very Short Answer Questions

Q1. Define resolution of vectors.

Answer: Splitting a vector into components along different directions.

Q2. What is unit vector?

Answer: A vector with magnitude 1 that shows direction only.

Q3. Name unit vectors.

Answer: î, ĵ, k̂

3. Short Answer Questions

Q1. Write vector in component form.

Answer: A = Ax î + Ay ĵ

Q2. Why are components useful?

Answer: They simplify calculations in physics problems.

4. Long Answer Questions

Q1. Explain resolution of vector in 2D.

A vector A making angle θ with x-axis can be resolved into components:
Ax = A cosθ
Ay = A sinθ
A = Ax î + Ay ĵ
Magnitude: A = √(Ax² + Ay²)

5. Assertion and Reason

Q1.

Assertion: Unit vectors have magnitude 1.
Reason: They are used to represent direction only.

Answer: Both are true and Reason is correct explanation.

6. Fill in the Blanks

Q1. Resolution means splitting vector into ______.

Answer: components

Q2. Unit vector along y-axis is ______.

Answer: ĵ

7. Match the Column

î → x-axis
ĵ → y-axis
k̂ → z-axis
Ax → x-component

8. Case Study

A force of 20 N makes 30° with x-axis.

Q1. Find Ax

Answer: Ax = 20 cos30 = 10√3 N

Q2. Find Ay

Answer: Ay = 20 sin30 = 10 N

9. Numericals

Q1. Find magnitude of vector (3,4)

Answer: √(3² + 4²) = 5