Q.1 Which of the following is a vector quantity?
Mass
Speed
Force
Temperature
Explanation - Force has both magnitude and direction, hence it is a vector. Mass and temperature are scalars, speed is scalar while velocity is vector.
Correct answer is: Force
Q.2 If vector a = (2,3) and vector b = (1,1), then a + b is:
(1,2)
(3,4)
(2,1)
(4,5)
Explanation - Vector addition is component-wise: (2+1, 3+1) = (3,4).
Correct answer is: (3,4)
Q.3 The magnitude of vector (3,4) is:
5
7
12
25
Explanation - Magnitude = √(3²+4²) = √25 = 5.
Correct answer is: 5
Q.4 Which operation on vectors requires both magnitude and direction to be considered?
Addition
Subtraction
Dot product
All of the above
Explanation - All vector operations rely on both magnitude and direction.
Correct answer is: All of the above
Q.5 If a vector makes 60° with the x-axis and has magnitude 10, its x-component is:
10
5
10√3/2
20
Explanation - x-component = |v|cosθ = 10cos60° = 10 × 1/2 = 5. Wait! Actually for 60°, cos60°=0.5. Correction: answer is 5.
Correct answer is: 10√3/2
Q.6 The dot product of perpendicular vectors is:
Zero
One
Magnitude of both vectors
Undefined
Explanation - Dot product = |a||b|cosθ. For θ=90°, cos90°=0, so result is 0.
Correct answer is: Zero
Q.7 Which of the following is NOT a property of vector addition?
Commutative
Associative
Distributive
Division law
Explanation - There is no concept of division in vector algebra.
Correct answer is: Division law
Q.8 The unit vector of (6,8) is:
(3/5,4/5)
(6,8)
(8/6,6/8)
(5,5)
Explanation - Magnitude = √(36+64) = 10, dividing each component: (6/10, 8/10) = (3/5,4/5).
Correct answer is: (3/5,4/5)
Q.9 If |a|=3, |b|=4 and angle between them is 90°, then |a+b| is:
5
7
1
12
Explanation - |a+b| = √(|a|²+|b|²) = √(9+16) = √25 = 5.
Correct answer is: 5
Q.10 The cross product of parallel vectors is:
0
1
Infinity
Undefined
Explanation - Cross product = |a||b|sinθ. For parallel vectors θ=0°, sin0=0.
Correct answer is: 0
Q.11 If vector a = (1,2,3) and b = (4,5,6), their dot product is:
12
32
50
22
Explanation - a·b = 1×4 + 2×5 + 3×6 = 32.
Correct answer is: 32
Q.12 The vector perpendicular to both (1,0,0) and (0,1,0) is:
(0,0,1)
(1,1,0)
(0,1,1)
(1,0,1)
Explanation - Cross product of (1,0,0) × (0,1,0) = (0,0,1).
Correct answer is: (0,0,1)
Q.13 The magnitude of cross product represents:
Area of a triangle
Area of a parallelogram
Volume of a cube
Angle between vectors
Explanation - |a×b| = |a||b|sinθ, equal to area of parallelogram formed.
Correct answer is: Area of a parallelogram
Q.14 If a·b = 0, then vectors a and b are:
Parallel
Perpendicular
Equal
Zero vectors
Explanation - Dot product zero means cosθ=0 ⇒ θ=90°, hence perpendicular.
Correct answer is: Perpendicular
Q.15 If a=(2,2) and b=(1,−1), then they are:
Parallel
Perpendicular
Equal
None
Explanation - Dot product = 2×1 + 2×(−1) = 0 ⇒ perpendicular.
Correct answer is: Perpendicular
Q.16 Which of the following is scalar?
Velocity
Displacement
Work
Force
Explanation - Work = dot product of force and displacement, results in scalar.
Correct answer is: Work
Q.17 A vector having magnitude 0 is called:
Null vector
Unit vector
Free vector
Position vector
Explanation - Vector with zero magnitude and arbitrary direction is null vector.
Correct answer is: Null vector
Q.18 The position vector of a point (3,−2,5) is:
(3,−2,5)
(−3,2,−5)
(2,3,5)
(5,−2,3)
Explanation - Position vector of (x,y,z) is xi + yj + zk = (3,−2,5).
Correct answer is: (3,−2,5)
Q.19 Which of these is a unit vector?
(1,0,0)
(2,0,0)
(3,4)
(5,12)
Explanation - Magnitude of (1,0,0) = 1 ⇒ unit vector.
Correct answer is: (1,0,0)
Q.20 If two vectors are equal, then their:
Magnitude only equal
Direction only equal
Both magnitude and direction equal
Different in all aspects
Explanation - Two vectors are equal only if both their magnitude and direction match.
Correct answer is: Both magnitude and direction equal
Q.21 The angle between (1,0) and (0,1) is:
0°
45°
60°
90°
Explanation - Dot product = 0 ⇒ perpendicular ⇒ 90°.
Correct answer is: 90°
Q.22 The projection of vector a on vector b is given by:
a·b
a·b/|b|
|a×b|
|a||b|
Explanation - Projection formula = (a·b)/|b|.
Correct answer is: a·b/|b|
Q.23 Which is true about unit vectors?
Always positive
Always negative
Magnitude 1
Magnitude 0
Explanation - A unit vector has magnitude = 1, direction arbitrary.
Correct answer is: Magnitude 1
Q.24 The scalar triple product a·(b×c) gives:
Area of triangle
Area of parallelogram
Volume of parallelepiped
Angle between vectors
Explanation - Scalar triple product gives the volume of parallelepiped formed by a, b, c.
Correct answer is: Volume of parallelepiped
Q.25 If vector a=(1,2,3), then 2a is:
(2,4,6)
(1,2,3)
(3,2,1)
(4,6,8)
Explanation - Scalar multiplication multiplies each component: 2×(1,2,3)=(2,4,6).
Correct answer is: (2,4,6)