Q.1 If two vectors A and B are perpendicular, what is the value of A · B?
|A||B|
0
1
|A|/|B|
Explanation - The dot product of two perpendicular vectors is zero because cos(90°) = 0.
Correct answer is: 0
Q.2 The magnitude of the resultant of two equal vectors inclined at 120° is:
Equal to each vector
Twice each vector
Zero
√3 times each vector
Explanation - Resultant R = √(A² + B² + 2ABcosθ). With A=B, θ=120°, R= A.
Correct answer is: Equal to each vector
Q.3 If vector A = 2i + 3j and vector B = i - j, then A · B is:
1
-1
5
-5
Explanation - Dot product = (2×1) + (3×-1) = 2 - 3 = -1.
Correct answer is: -1
Q.4 Which of the following is a scalar quantity?
Velocity
Force
Displacement
Work
Explanation - Work is a scalar product of force and displacement, hence scalar.
Correct answer is: Work
Q.5 The unit vector in the direction of i + j is:
(i + j)/√2
(i + j)/2
(i + j)
(i - j)/√2
Explanation - Magnitude of i+j is √(1²+1²)=√2, so unit vector = (i+j)/√2.
Correct answer is: (i + j)/√2
Q.6 If |A| = 3, |B| = 4 and angle between them is 90°, the magnitude of A×B is:
7
12
1
25
Explanation - |A×B| = |A||B|sinθ = 3×4×sin90° = 12.
Correct answer is: 12
Q.7 Two vectors are equal if:
They have same magnitude only
They have same direction only
They have same magnitude and direction
They originate from same point
Explanation - Equality of vectors requires both magnitude and direction to be identical.
Correct answer is: They have same magnitude and direction
Q.8 If cosθ = A·B / (|A||B|), then θ is:
Angle between A and B
Magnitude of A
Magnitude of B
Projection of A on B
Explanation - This formula defines the angle between two vectors.
Correct answer is: Angle between A and B
Q.9 The projection of vector A on B is given by:
A·B/|A|
A·B/|B|
|A||B|
|A×B|
Explanation - Projection of A on B = (A·B)/|B|.
Correct answer is: A·B/|B|
Q.10 If A = 3i + 4j, what is the magnitude of A?
5
7
25
12
Explanation - Magnitude = √(3²+4²) = √25 = 5.
Correct answer is: 5
Q.11 Which of the following operations is not defined for vectors?
Addition
Subtraction
Division
Cross product
Explanation - Vectors cannot be divided directly like scalars.
Correct answer is: Division
Q.12 If vector A = i + j and B = i - j, then A×B is:
2k
-2k
0
i+j
Explanation - Cross product = (i+j)×(i-j) = -i×j + j×i = 2k.
Correct answer is: 2k
Q.13 The vector product of two parallel vectors is:
Maximum
Zero
Equal to product of magnitudes
Undefined
Explanation - Cross product is |A||B|sinθ, with θ=0°, sin0=0.
Correct answer is: Zero
Q.14 If A·B = 0, which is true?
A=0
B=0
A and B are parallel
A and B are perpendicular
Explanation - Dot product zero implies angle between vectors is 90°.
Correct answer is: A and B are perpendicular
Q.15 The vector having magnitude 1 is called:
Zero vector
Unit vector
Position vector
Scalar
Explanation - A vector of magnitude 1 is called unit vector.
Correct answer is: Unit vector
Q.16 Which one of the following is true for scalars?
They have magnitude and direction
They have only magnitude
They have only direction
They are always positive
Explanation - Scalars are physical quantities with only magnitude.
Correct answer is: They have only magnitude
Q.17 The magnitude of (i + j + k) is:
1
√2
√3
3
Explanation - Magnitude = √(1²+1²+1²) = √3.
Correct answer is: √3
Q.18 If A = 2i - 3j, then the direction cosines are proportional to:
2 and 3
2 and -3
-2 and 3
3 and 2
Explanation - Direction cosines are proportional to the components of vector.
Correct answer is: 2 and -3
Q.19 Which law is applicable to the addition of vectors?
Law of sines
Law of cosines
Parallelogram law
Law of inertia
Explanation - Vector addition follows parallelogram law.
Correct answer is: Parallelogram law
Q.20 The scalar triple product A·(B×C) gives:
Area of triangle
Volume of parallelepiped
Work done
Torque
Explanation - Scalar triple product represents volume of parallelepiped formed by vectors.
Correct answer is: Volume of parallelepiped
Q.21 The minimum number of vectors required to give a resultant of zero is:
2
3
4
Any number
Explanation - Two equal and opposite vectors give a resultant zero.
Correct answer is: 2
Q.22 The position vector of a point (2, -3, 1) is:
2i + 3j + k
2i - 3j + k
-2i + 3j + k
2i + 3j - k
Explanation - Position vector = xi + yj + zk = 2i - 3j + k.
Correct answer is: 2i - 3j + k
Q.23 If A = 2i + j and B = i - 3j, the magnitude of A+B is:
√13
√17
√10
√20
Explanation - A+B = 3i - 2j; magnitude = √(9+4) = √13 (Correction: Actually √13).
Correct answer is: √17
Q.24 The result of adding two vectors at right angles is:
Arithmetic sum
Geometric mean
Resultant by Pythagoras theorem
Zero
Explanation - For perpendicular vectors, resultant magnitude = √(A²+B²).
Correct answer is: Resultant by Pythagoras theorem
Q.25 Which one of the following is a vector?
Speed
Mass
Temperature
Acceleration
Explanation - Acceleration has both magnitude and direction, hence vector.
Correct answer is: Acceleration