100 High-Scoring MCQs on Vectors and Equilibrium (Set - 2) | Class 11 Physics | Unit 2 | FBISE 



This post contains 100 carefully selected multiple-choice questions (MCQs) from Unit-2: Vectors and Equilibrium of Class 11 Physics, designed strictly according to the FBISE syllabus. These MCQs include a well-balanced mix of conceptual and numerical problems, making them exam-ready, revision-friendly, and high-scoring.

Whether you are preparing for annual board examinations, chapter tests, or competitive entry tests, this comprehensive MCQ collection thoroughly covers all the fundamental principles of vectors, torque, and equilibrium, enabling students to master the chapter with confidence and accuracy.

This unit-wise MCQ set includes questions from:

  • Description of Cartesian coordinate system and vector representation
  • Determination of vector sum using head-to-tail and parallelogram methods
  • Resolution of vectors into perpendicular components and their numerical applications
  • Scalar (dot) product of vectors and its relation to the angle between vectors
  • Vector (cross) product and its magnitude and direction using the right-hand rule
  • Torque as a vector product (r × F) and applications of torque in real life
  • First condition of equilibrium (net force = 0) and second condition of equilibrium (net torque = 0)
  • Two-dimensional statics problems solved using the conditions of equilibrium
  • Applications of vectors and equilibrium principles in daily life, engineering, and mechanics

Each MCQ is provided with the correct answer and a clear, concise explanation, helping students:

  • Strengthen conceptual understanding of vectors and equilibrium
  • Avoid common exam mistakes in numerical and conceptual questions
  • Improve problem-solving skills involving forces, torque, and vector operations
  • Achieve maximum marks in the MCQs section

This all-in-one MCQ collection is an essential tool for Class 11 students aiming to excel in physics exams and fully master the concepts of vectors and equilibrium.


MCQs No. 1

If Rx is positive and Ry is positive, then θ lies in ______ quadrant.

a. 1st
b. 2nd
c. 3rd
d. 4th

The Correct Answer is a. 1st

Explanation:
When both X and Y components are positive, the vector lies in the first quadrant (0°–90°).


MCQs No. 2

If Rx is negative and Ry is positive, then θ lies in ______ quadrant.

a. 1st
b. 2nd
c. 3rd
d. 4th

The Correct Answer is b. 2nd

Explanation:
Negative X and positive Y place the vector in the second quadrant.


MCQs No. 3

A vector is a mathematical tool having both magnitude and:

a. Direction

b. Power

c. Density

d. Mass

The Correct Answer is: Direction

Explanation:

vector is defined by its magnitude and direction.


MCQs No. 4

The magnitude of a vector R with components Rx and Ry is given by:

a. R = Rx + Ry
b. R = Rx − Ry
c. R = √(Rx² + Ry²)
d. R = Rx × Ry

The Correct Answer is c.

Explanation:
Resultant magnitude follows Pythagoras theorem.


MCQs No. 5

The angle θ of a vector with x-axis is given by:

a. tan θ = Ry / Rx
b. tan θ = Rx / Ry
c. sin θ = Rx / Ry
d. cos θ = Ry / Rx

The Correct Answer is a.

Explanation:
tanθ = vertical component / horizontal component.


MCQs No. 6

Head-to-tail rule is used to determine:

a. Difference of vectors
b. Product of vectors
c. Sum of vectors
d. Division of vectors

The Correct Answer is c.

Explanation:
Head-to-tail method is for vector addition.


MCQs No. 7

A vector can be resolved into components that are:

a. Parallel
b. Random
c. Perpendicular
d. Opposite

The Correct Answer is c.

Explanation:
Vectors are usually resolved into perpendicular components.


MCQs No. 8

The scalar product of two vectors A and B is:

a. AB sinθ
b. AB cosθ
c. A/B
d. A×B

The Correct Answer is b.

Explanation:
Dot product = AB cosθ.


MCQs No. 9

Scalar product of two perpendicular vectors is:

a. Maximum
b. Zero
c. Minimum
d. Infinite

The Correct Answer is b.

Explanation:
cos 90° = 0.


MCQs No. 10

The vector product of two vectors A and B is:

a. AB cosθ
b. AB sinθ
c. A + B
d. A − B

The Correct Answer is b.

Explanation:
Cross product magnitude = AB sinθ.


MCQs No. 11

The direction of vector product is determined by:

a. Fleming’s left hand rule
b. Fleming’s right hand rule
c. Right-hand thumb rule
d. Lenz’s law

The Correct Answer is c.

Explanation:
Right-hand thumb rule gives direction of cross product.


MCQs No. 12

Torque is defined as:

a. F × r
b. r × F
c. r + F
d. r / F

The Correct Answer is b.

Explanation:
Torque = r × F.


MCQs No. 13

The SI unit of torque is:

a. Newton
b. Joule
c. Newton-meter
d. Watt

The Correct Answer is c.

Explanation:
Torque is measured in N·m.


MCQs No. 14

Torque is a:

a. Scalar quantity
b. Vector quantity
c. Tensor
d. Dimensionless quantity

The Correct Answer is b.

Explanation:
Torque has both magnitude and direction.


MCQs No. 15

First condition of equilibrium states that:

a. ∑τ = 0
b. ∑F = 0
c. ∑v = 0
d. ∑a = 0

The Correct Answer is b.

Explanation:
Net force must be zero.


MCQs No. 16

Second condition of equilibrium states that:

a. ∑F = 0
b. ∑τ = 0
c. v = 0
d. a = 0

The Correct Answer is b.

Explanation:
Net torque must be zero.


MCQs No. 17

A body is in complete equilibrium if:

a. ∑F = 0
b. ∑τ = 0
c. Both ∑F = 0 and ∑τ = 0
d. v is constant

The Correct Answer is c.

Explanation:
Both conditions must be satisfied.


MCQs No. 18

If two forces of 3 N and 4 N act at right angles, resultant force is:

a. 5 N
b. 7 N
c. 1 N
d. 12 N

The Correct Answer is a.

Explanation:
R = √(3² + 4²) = 5 N.


MCQs No. 19

If a force of 10 N acts at a distance of 2 m, torque is:

a. 5 N·m
b. 20 N·m
c. 12 N·m
d. 2 N·m

The Correct Answer is b.

Explanation:
τ = rF = 2 × 10 = 20 N·m.


MCQs No. 20

The dot product of two parallel vectors is:

a. Zero
b. Maximum
c. Minimum
d. Undefined

The Correct Answer is b.

Explanation:
cos 0° = 1 → dot product is maximum.


MCQs No. 21

A vector of magnitude 10 N makes an angle 30° with x-axis. Its x-component is:

a. 5 N
b. 8.66 N
c. 10 N
d. 0 N

The Correct Answer is b. 8.66 N

Explanation:
Rx = R cosθ = 10 cos30° = 8.66 N.


MCQs No. 22

A vector of 20 N makes an angle 60° with x-axis. Its y-component is:

a. 10 N
b. 17.32 N
c. 20 N
d. 5 N

The Correct Answer is b. 17.32 N

Explanation:
Ry = R sin60° = 20 × 0.866 = 17.32 N.


MCQs No. 23

Two vectors A and B are parallel. The angle between them is:

a. 0°
b. 45°
c. 90°
d. 180°

The Correct Answer is a. 0°

Explanation:
Parallel vectors have zero angle.


MCQs No. 24

Two vectors are antiparallel. The angle between them is:

a. 0°
b. 90°
c. 180°
d. 270°

The Correct Answer is c. 180°

Explanation:
Antiparallel means opposite direction.


MCQs No. 25

The dot product of perpendicular vectors is:

a. Maximum
b. Zero
c. Minimum
d. Infinite

The Correct Answer is b. Zero

Explanation:
cos 90° = 0.


MCQs No. 26

The cross product of parallel vectors is:

a. Maximum
b. Zero
c. Infinite
d. Undefined

The Correct Answer is b. Zero

Explanation:
sin 0° = 0.


MCQs No. 27

The unit of scalar product is:

a. N
b. N/m
c. Depends on vectors
d. Always dimensionless

The Correct Answer is c.

Explanation:
Depends on physical quantities involved.


MCQs No. 28

The unit of vector product is:

a. Scalar unit
b. Same as product of vectors
c. Dimensionless
d. Always Newton

The Correct Answer is b.

Explanation:
Cross product has units of multiplication of vectors.


MCQs No. 29

A force of 5 N acts perpendicular to a rod of length 2 m. Torque is:

a. 2.5 N·m
b. 10 N·m
c. 5 N·m
d. 20 N·m

The Correct Answer is b. 10 N·m

Explanation:
τ = rF = 2 × 5 = 10 N·m.


MCQs No. 30

If force acts along the rod, torque will be:

a. Maximum
b. Zero
c. Minimum
d. Negative

The Correct Answer is b. Zero

Explanation:
sin 0° = 0.


MCQs No. 31

Torque is maximum when angle between r and F is:

a. 0°
b. 30°
c. 45°
d. 90°

The Correct Answer is d. 90°

Explanation:
sin90° = 1 gives maximum torque.


MCQs No. 32

A body is in translational equilibrium if:

a. ∑τ = 0
b. ∑F = 0
c. v = 0
d. a ≠ 0

The Correct Answer is b.

Explanation:
Net force must be zero.


MCQs No. 33

A body is in rotational equilibrium if:

a. ∑F = 0
b. ∑τ = 0
c. v = constant
d. a = constant

The Correct Answer is b.

Explanation:
Net torque must be zero.


MCQs No. 34

A body is in static equilibrium if:

a. ∑F = 0
b. ∑τ = 0
c. Both ∑F = 0 and ∑τ = 0
d. v is maximum

The Correct Answer is c.

Explanation:
Both conditions must be satisfied.


MCQs No. 35

For which angle the equation AB=A×B is correct?

a. 90°

b. 60°

c. 45°

d. 35°

The Correct Answer is: 45°

Explanation:
AB=A×B  is true only when the angle between two vectors is 45° because sin45°=cos45°



MCQs No. 36

 If two forces are equal and opposite, resultant force is:

a. Zero
b. Maximum
c. Minimum
d. Infinite

The Correct Answer is a. Zero

Explanation:
They cancel each other.


MCQs No. 37

The scalar product gives information about:

a. Direction only
b. Magnitude only
c. Angle between vectors
d. Torque

The Correct Answer is c.

Explanation:
Dot product depends on cosθ.


MCQs No. 38

The vector product gives information about:

a. Work done
b. Power
c. Area and direction
d. Temperature

The Correct Answer is c.

Explanation:
Cross product relates to area and perpendicular direction.


MCQs No. 39

What is the angle between A and B for which A+B=AB∣ ?

a. 30°

b. 90°

c. 45°

d. 60°

The Correct Answer is: 90°

Explanation:
Condition A+B=AB is true only if A and B

 are perpendicular.


MCQs No. 40

The origin of Cartesian system is:

a. (1,0)
b. (0,1)
c. (0,0)
d. (1,1)

The Correct Answer is c.

Explanation:
Origin is (0,0).


MCQs No. 41

If Rx = 0 and Ry ≠ 0, the vector lies on:

a. X-axis
b. Y-axis
c. Origin
d. Quadrant

The Correct Answer is b.

Explanation:
No x-component → on y-axis.


MCQs No. 42

If Ry = 0 and Rx ≠ 0, vector lies on:

a. X-axis
b. Y-axis
c. Origin
d. Quadrant

The Correct Answer is a.

Explanation:
No y-component → on x-axis.


MCQs No. 43

The resultant of vectors is found by:

a. Multiplication
b. Division
c. Addition
d. Subtraction only

The Correct Answer is c.

Explanation:
Vector addition gives resultant.


MCQs No. 44

Parallelogram law is used for:

a. Multiplication of vectors
b. Division of vectors
c. Addition of vectors
d. Subtraction of vectors

The Correct Answer is c.

Explanation:
Parallelogram law finds resultant.


MCQs No. 45

If Rx  is positive and Ry  is negative, then θ  lies in:

a. 1st quadrant

b. 2nd quadrant

c. 3rd quadrant

d. 4th quadrant

The Correct Answer is: 4th quadrant

Explanation:

If X-component is positive and Y-component negative, the vector lies in 4th quadrant, making an angle between 270° and 360° with positive X-axis.


MCQs No. 46

The cross product is a:

a. Scalar
b. Vector
c. Tensor
d. Dimensionless

The Correct Answer is b.

Explanation:
Cross product produces a vector.


MCQs No. 47

The dot product is a:

a. Vector
b. Scalar
c. Tensor
d. Matrix

The Correct Answer is b.

Explanation:
Dot product gives scalar.


MCQs No. 48

Magnitude of the resultant of two vectors of equal magnitude is zero, then the angle between them is:

a. 0°

b. 90°

c. 120°

d. 180°

The Correct Answer is: 180°

Explanation:

Two vectors give zero resultant only if they are equal in magnitude and opposite in direction (angle = 180°).


MCQs No. 49

The cross product of A=3ı^+2ȷ^+k^  and B=2ı^ȷ^+3k^  is:

a. 7ı^7ȷ^7k^ 

b. 7ı^+7ȷ^+7k^ 

c. 7ı^+7ȷ^7k^ 

d. 7ı^7ȷ^7k^ 

The Correct Answer is: 7ı^7ȷ^7k^ 

Explanation:

A×B=ı^ȷ^k^321213=7ı^7ȷ^7k^



MCQs No. 50

Torque depends on:

a. Force only
b. Distance only
c. Angle only
d. Force, distance, and angle

The Correct Answer is d.

Explanation:
τ = rF sinθ.


MCQs No. 51

If a vector has magnitude 10 N and makes an angle 90° with x-axis, its x-component is:

a. 10 N
b. 5 N
c. 0 N
d. −10 N

The Correct Answer is c. 0 N

Explanation:
Rx = R cos90° = 0.


MCQs No. 52

If a vector has magnitude 10 N and makes an angle 0° with x-axis, its y-component is:

a. 10 N
b. 5 N
c. 0 N
d. −10 N

The Correct Answer is c. 0 N

Explanation:
Ry = R sin0° = 0.


MCQs No. 53

Two vectors have dot product zero. They are:

a. Parallel
b. Perpendicular
c. Opposite
d. Same

The Correct Answer is b.

Explanation:
Dot product zero means θ = 90°.


MCQs No. 54

Two vectors have cross product zero. They are:

a. Perpendicular
b. Parallel
c. At 45°
d. Random

The Correct Answer is b.

Explanation:
sin0° = 0 for parallel vectors.


MCQs No. 55

The magnitude of cross product is maximum when angle is:

a. 0°
b. 30°
c. 60°
d. 90°

The Correct Answer is d.

Explanation:
sin90° = 1 (maximum).


MCQs No. 56

The magnitude of dot product is maximum when angle is:

a. 0°
b. 45°
c. 90°
d. 180°

The Correct Answer is a.

Explanation:
cos0° = 1 (maximum).


MCQs No. 57

If three forces acting on a body are in equilibrium, their vector sum is:

a. Maximum
b. Minimum
c. Zero
d. Infinite

The Correct Answer is c.

Explanation:
Net force must be zero.


MCQs No. 58

If torque is zero, body will:

a. Rotate with acceleration
b. Rotate uniformly
c. Not rotate
d. Translate

The Correct Answer is c.

Explanation:
No torque → no rotation.


MCQs No. 59

A spanner is long because:

a. To increase force
b. To increase torque
c. To decrease torque
d. For beauty

The Correct Answer is b.

Explanation:
Longer lever arm increases torque.


MCQs No. 60

A door handle is fixed at the edge of the door to:

a. Decrease torque
b. Increase torque
c. Reduce friction
d. Increase mass

The Correct Answer is b.

Explanation:
Maximum distance from hinge increases torque.


MCQs No. 61

The unit vector has magnitude:

a. 0
b. 1
c. Infinite
d. Depends

The Correct Answer is b.

Explanation:
Unit vector magnitude = 1.


MCQs No. 62

The resultant of two opposite equal vectors is:

a. A
b. 2A
c. Zero
d. √2A

The Correct Answer is c.

Explanation:
They cancel each other.


MCQs No. 63

The angle between a vector and its negative is:

a. 0°
b. 45°
c. 90°
d. 180°

The Correct Answer is d.

Explanation:
Negative vector is opposite direction.


MCQs No. 64

If R = A + B and A = −B, then R is:

a. Maximum
b. Minimum
c. Zero
d. Infinite

The Correct Answer is c.

Explanation:
Equal and opposite vectors cancel.


MCQs No. 65

The work done is maximum when angle between force and displacement is:

a. 0°
b. 45°
c. 90°
d. 180°

The Correct Answer is a.

Explanation:
Dot product maximum at 0°.


MCQs No. 66

The work done is zero when angle between force and displacement is:

a. 0°
b. 45°
c. 90°
d. 180°

The Correct Answer is c.

Explanation:
cos90° = 0.


MCQs No. 67

The vector product is used to calculate:

a. Work
b. Power
c. Torque
d. Energy

The Correct Answer is c.

Explanation:
Torque = r × F.


MCQs No. 68

If r = 3 m and F = 10 N, torque when force is perpendicular is:

a. 10 N·m
b. 20 N·m
c. 30 N·m
d. 5 N·m

The Correct Answer is c.

Explanation:
τ = rF = 3 × 10 = 30 N·m.


MCQs No. 69

If angle between r and F is 0°, torque is:

a. Maximum
b. Zero
c. Minimum
d. Negative

The Correct Answer is b.

Explanation:
sin0° = 0.


MCQs No. 70

The polygon law of vectors is an extension of:

a. Triangle law
b. Parallelogram law
c. Circular law
d. Head law

The Correct Answer is a.

Explanation:
Polygon law is extended triangle law.


MCQs No. 71

The direction of cross product is perpendicular to:

a. A only
b. B only
c. Both A and B
d. Neither

The Correct Answer is c.

Explanation:
Cross product is perpendicular to both vectors.


MCQs No. 72

If Rx = 3 and Ry = 4, resultant magnitude is:

a. 5
b. 7
c. 12
d. 1

The Correct Answer is a.

Explanation:
R = √(3² + 4²) = 5.


MCQs No. 73

If resultant force is zero, acceleration is:

a. Maximum
b. Minimum
c. Zero
d. Infinite

The Correct Answer is c.

Explanation:
Newton’s second law.


MCQs No. 74

If two forces act at 60°, resultant is:

a. F1 + F2
b. √(F1² + F2²)
c. √(F1² + F2² + 2F1F2 cos60°)
d. F1F2

The Correct Answer is c.

Explanation:
Law of cosines for vector addition.


MCQs No. 75

The angle between two vectors is obtained from:

a. Cross product
b. Dot product
c. Torque
d. Force

The Correct Answer is b.

Explanation:
Dot product involves cosθ.


MCQs No. 76

The moment arm is:

a. Force
b. Distance from axis
c. Velocity
d. Acceleration

The Correct Answer is b.

Explanation:
Perpendicular distance from pivot.


MCQs No. 77

If three coplanar forces are in equilibrium, they must be:

a. Parallel
b. Concurrent
c. Collinear
d. Random

The Correct Answer is b.

Explanation:
For equilibrium, forces must be concurrent.


MCQs No. 78

The equilibrium of a body depends on:

a. Force only
b. Torque only
c. Both force and torque
d. Velocity

The Correct Answer is c.

Explanation:
Both conditions must be satisfied.


MCQs No. 79

The SI unit of force is:

a. Joule
b. Newton
c. Watt
d. Pascal

The Correct Answer is b.

Explanation:
Force unit is Newton.


MCQs No. 80

The SI unit of distance is:

a. Kilometer
b. Centimeter
c. Meter
d. Millimeter

The Correct Answer is c.

Explanation:
Base unit of length is meter.


MCQs No. 81

If two vectors are perpendicular, their dot product is:

a. AB
b. AB/2
c. 0
d. Infinite

The Correct Answer is c.

Explanation:
cos90° = 0.


MCQs No. 82

If two vectors are parallel, their cross product is:

a. AB
b. AB/2
c. 0
d. Infinite

The Correct Answer is c.

Explanation:
sin0° = 0.


MCQs No. 83

A body in equilibrium has acceleration:

a. Maximum
b. Minimum
c. Zero
d. Infinite

The Correct Answer is c.

Explanation:
Net force zero → acceleration zero.


MCQs No. 84

If a force acts at the pivot point, torque is:

a. Maximum
b. Zero
c. Minimum
d. Negative

The Correct Answer is b.

Explanation:
r = 0 → τ = 0.


MCQs No. 85

The longer the lever arm, the:

a. Smaller torque
b. Larger torque
c. No torque
d. Constant torque

The Correct Answer is b.

Explanation:
τ = rF.


MCQs No. 86

The unit of angle is:

a. Newton
b. Radian
c. Joule
d. Watt

The Correct Answer is b.

Explanation:
SI unit of angle is radian.


MCQs No. 87

If F1 = 6 N and F2 = 8 N at right angles, resultant is:

a. 10 N
b. 12 N
c. 2 N
d. 14 N

The Correct Answer is a.

Explanation:
R = √(6² + 8²) = 10 N.


MCQs No. 88

If torque is clockwise, it is taken as:

a. Positive
b. Negative
c. Zero
d. Infinite

The Correct Answer is b.

Explanation:
Convention: clockwise negative.


MCQs No. 89

If torque is anticlockwise, it is taken as:

a. Positive
b. Negative
c. Zero
d. Infinite

The Correct Answer is a.

Explanation:
Convention: anticlockwise positive.


MCQs No. 90

A vector having zero magnitude is called:

a. Unit vector
b. Null vector
c. Negative vector
d. Parallel vector

The Correct Answer is b.

Explanation:
Zero vector is null vector.


MCQs No. 91

The sum of all forces in equilibrium is:

a. Maximum
b. Minimum
c. Zero
d. Infinite

The Correct Answer is c.

Explanation:
∑F = 0.


MCQs No. 92

The sum of all torques in equilibrium is:

a. Maximum
b. Minimum
c. Zero
d. Infinite

The Correct Answer is c.

Explanation:
∑τ = 0.


MCQs No. 93

The angle between two perpendicular axes is:

a. 0°
b. 45°
c. 90°
d. 180°

The Correct Answer is c.

Explanation:
Axes are perpendicular.


MCQs No. 94

The x-axis is horizontal and y-axis is:

a. Horizontal
b. Vertical
c. Inclined
d. Circular

The Correct Answer is b.

Explanation:
Standard Cartesian system.


MCQs No. 95

The direction of resultant vector is found by:

a. R = √(Rx² + Ry²)
b. tanθ = Ry/Rx
c. sinθ = Ry/R
d. cosθ = Rx/R

The Correct Answer is b.

Explanation:
tanθ = Ry/Rx.


MCQs No. 96

The perpendicular components of a vector are:

a. Equal
b. Opposite
c. Independent
d. Dependent

The Correct Answer is c.

Explanation:
Components are independent.


MCQs No. 97

If a body is in equilibrium, velocity is:

a. Zero
b. Constant or zero
c. Maximum
d. Infinite

The Correct Answer is b.

Explanation:
Equilibrium may be static or dynamic.


MCQs No. 98

The triangle law of vectors is used to find:

a. Difference
b. Product
c. Sum
d. Ratio

The Correct Answer is c.

Explanation:
Triangle law gives vector addition.


MCQs No. 99

The magnitude of a vector is always:

a. Positive
b. Negative
c. Zero only
d. Imaginary

The Correct Answer is a.

Explanation:
Magnitude cannot be negative.


MCQs No. 100

The equilibrium of a body means:

a. It must be at rest
b. It must move with acceleration
c. Net force and net torque are zero
d. It must move in circle

The Correct Answer is c.

Explanation:
Both conditions of equilibrium must be satisfied.