Q.1 Which of the following is a vector quantity?
Speed
Work
Displacement
Mass
Explanation - Displacement has both magnitude and direction, making it a vector quantity.
Correct answer is: Displacement
Q.2 The magnitude of the resultant of two vectors is maximum when the angle between them is:
0°
90°
180°
45°
Explanation - When two vectors are in the same direction, their resultant is the sum of their magnitudes, giving the maximum value.
Correct answer is: 0°
Q.3 If two vectors are equal in magnitude but opposite in direction, their resultant is:
Zero
Double the magnitude
Half the magnitude
Infinite
Explanation - Equal and opposite vectors cancel each other, giving zero resultant.
Correct answer is: Zero
Q.4 The scalar product of two perpendicular vectors is:
Zero
One
Product of magnitudes
Undefined
Explanation - The dot product is |A||B|cosθ. For perpendicular vectors θ = 90°, cos90° = 0, so the result is zero.
Correct answer is: Zero
Q.5 The unit vector along the x-axis is:
î
ĵ
k̂
0
Explanation - The standard unit vector along x-axis is represented by î.
Correct answer is: î
Q.6 If a = 3î + 4ĵ, then |a| equals:
7
5
12
1
Explanation - Magnitude of vector = √(3² + 4²) = √25 = 5.
Correct answer is: 5
Q.7 Which one of the following is NOT a vector?
Force
Acceleration
Momentum
Energy
Explanation - Energy is scalar because it has magnitude but no direction.
Correct answer is: Energy
Q.8 If |A| = 5 and |B| = 12, and they are perpendicular, then |A × B| equals:
60
17
13
5
Explanation - Cross product magnitude = |A||B|sin90° = 5 × 12 = 60.
Correct answer is: 60
Q.9 The projection of vector A on B is given by:
A·B / |B|
|A||B|cosθ
A×B
|A||B|sinθ
Explanation - Projection of A on B is (A·B)/|B|, which represents the component of A along B.
Correct answer is: A·B / |B|
Q.10 The angle between two vectors is zero when:
They are parallel
They are perpendicular
They are opposite
They are arbitrary
Explanation - Two vectors are said to have zero angle when they are parallel and point in the same direction.
Correct answer is: They are parallel
Q.11 The cross product of two parallel vectors is:
Zero
Product of magnitudes
Sum of magnitudes
Undefined
Explanation - Cross product = |A||B|sinθ. For parallel vectors θ = 0°, so sin0 = 0.
Correct answer is: Zero
Q.12 If A = î + 2ĵ and B = 2î + ĵ, then A·B equals:
4
5
10
2
Explanation - Dot product = (1)(2) + (2)(1) = 2 + 2 = 4.
Correct answer is: 4
Q.13 Which of the following represents a unit vector?
(3î + 4ĵ)/5
î + ĵ
2î + 2ĵ
5î
Explanation - Unit vector has magnitude 1. (3/5, 4/5) has magnitude √((3/5)² + (4/5)²) = 1.
Correct answer is: (3î + 4ĵ)/5
Q.14 The condition for two vectors to be perpendicular is:
A·B = 0
A×B = 0
|A| = |B|
They are parallel
Explanation - Two vectors are perpendicular when their dot product is zero.
Correct answer is: A·B = 0
Q.15 Which of the following is NOT true?
Work is a scalar
Force is a vector
Displacement is a scalar
Velocity is a vector
Explanation - Displacement is a vector, not a scalar.
Correct answer is: Displacement is a scalar
Q.16 If A = 2î and B = 3ĵ, then A·B is:
6
0
5
1
Explanation - Dot product = (2)(0) + (0)(3) = 0. They are perpendicular.
Correct answer is: 0
Q.17 The unit vector perpendicular to both î and ĵ is:
k̂
-k̂
î
ĵ
Explanation - î × ĵ = k̂, which is perpendicular to both.
Correct answer is: k̂
Q.18 A vector of magnitude 10 makes an angle of 60° with the x-axis. Its x-component is:
10
5
8.66
6
Explanation - X-component = 10 cos60° = 10 × 0.5 = 5.
Correct answer is: 5
Q.19 Which law is used to add two non-parallel vectors?
Triangle law
Newton's law
Ohm's law
Hooke's law
Explanation - The triangle law of vector addition is used to add two non-parallel vectors.
Correct answer is: Triangle law
Q.20 If two vectors A and B are such that A × B = 0, then they are:
Parallel
Perpendicular
Equal
Zero
Explanation - Cross product is zero if vectors are parallel or one is zero.
Correct answer is: Parallel
Q.21 Which of the following has dimensions of a vector?
Torque
Pressure
Temperature
Energy
Explanation - Torque is a vector quantity as it has direction (moment of force).
Correct answer is: Torque
Q.22 The magnitude of vector 2î + 2ĵ + 2k̂ is:
2
6
√12
√8
Explanation - Magnitude = √(2² + 2² + 2²) = √12.
Correct answer is: √12
Q.23 The direction cosines of a unit vector satisfy:
l² + m² + n² = 0
l² + m² + n² = 1
l + m + n = 1
l + m + n = 0
Explanation - For a unit vector, the sum of squares of direction cosines equals 1.
Correct answer is: l² + m² + n² = 1
Q.24 The vector product of two vectors gives a result that is:
Scalar
Vector
Unitless
Always zero
Explanation - Cross product results in a vector perpendicular to the plane of the two vectors.
Correct answer is: Vector
Q.25 Which quantity can be represented as the product of a scalar and a unit vector?
Velocity
Force
Displacement
All of these
Explanation - Any vector can be written as magnitude (scalar) × direction (unit vector).
Correct answer is: All of these