Scalars and vectors, vector addition and subtraction, scalar and vector products, unit vector - Question Bank

1. Which of the following represents the zero vector?
A) A vector with zero magnitude
B) A vector with zero direction
C) A vector with zero magnitude and undefined direction
D) A vector with magnitude 1
2. The angle that a vector A = Ax i + Ay j makes with the positive x-axis is given by:
A) tan(theta) = Ay / Ax
B) tan(theta) = Ax / Ay
C) cos(theta) = Ax / |A|
D) sin(theta) = Ay / |A|
3. If a vector has components Ax = 5 and Ay = -12, its magnitude is:
A) 5
B) 12
C) 13
D) 17
4. Which of the following is a correct representation of a vector in component form?
A) A = Ax + Ay
B) A = Ax i + Ay j
C) A = Ax / i + Ay / j
D) A = Ax - Ay
5. The direction of the resultant vector of two vectors A and B can be found using:
A) Scalar product
B) Vector product
C) Tangent of an angle involving their components
D) Magnitude of their sum
6. If A = 2i + 3j and B = -3i - 2j, what is the magnitude of A+B?
A) 0
B) 1
C) sqrt(2)
D) 2
7. If A = 2i + 3j and B = -3i - 2j, what is the scalar product A . B?
A) 0
B) -12
C) 13
D) -13
8. The vector sum of two vectors A and B is minimum when the angle between them is:
A) 0 degrees
B) 90 degrees
C) 180 degrees
D) 270 degrees
9. The vector sum of two vectors A and B is maximum when the angle between them is:
A) 0 degrees
B) 90 degrees
C) 180 degrees
D) 270 degrees
10. If A = 5i and B = 2i, what is the magnitude of A x B?
A) 0
B) 7
C) 10
D) 10i
11. If A = 5i and B = 2j, what is the magnitude of A x B?
A) 0
B) 7
C) 10
D) 10k
12. Which property is NOT satisfied by the vector product of two vectors?
A) Commutative property
B) Distributive property
C) Anticommutative property
D) None of the above
13. Which property is NOT satisfied by the scalar product of two vectors?
A) Commutative property
B) Distributive property
C) Associative property
D) None of the above
14. The direction of a vector can be indicated by:
A) Its length
B) An arrow head
C) Its magnitude
D) Its sign
15. A vector can be represented graphically by an arrow, where the length of the arrow represents:
A) The direction of the vector
B) The magnitude of the vector
C) The sign of the vector
D) The component of the vector
16. If the angle between two vectors A and B is 0 degrees, then A x B = ?
A) |A||B|
B) 0
C) -|A||B|
D) Undefined
17. If the angle between two vectors A and B is 90 degrees, then A . B = ?
A) |A||B|
B) 0
C) -|A||B|
D) Undefined
18. The resultant of two forces F1 and F2 acting at an angle theta is given by R. If the angle between F1 and F2 is increased, the magnitude of R will:
A) Increase
B) Decrease
C) Remain the same
D) Become zero
19. If two vectors have magnitudes 3 and 4, and the angle between them is 60 degrees, what is the magnitude of their vector product?
A) 6
B) 12
C) 7
D) 24
20. If two vectors have magnitudes 3 and 4, and the angle between them is 60 degrees, what is the magnitude of their scalar product?
A) 6
B) 12
C) 7
D) 24
21. The angle between vector A = i and vector B = -i is:
A) 0 degrees
B) 90 degrees
C) 180 degrees
D) 270 degrees
22. The angle between vector A = i and vector B = j is:
A) 0 degrees
B) 45 degrees
C) 90 degrees
D) 180 degrees
23. Let A = 2i + 3j and B = 4i - j. What is A x B? (Assuming 2D vectors in xy-plane, cross product yields a k component)
A) 11k
B) -11k
C) 5k
D) 0k
24. Let A = 2i + 3j and B = 4i - j. What is A . B?
A) 5
B) -5
C) 11
D) 10
25. Let A = i + j and B = i - j. What is A - B?
A) 2i
B) 2j
C) 0
D) i + j
26. Let A = i + j and B = i - j. What is A + B?
A) 2i
B) 2j
C) 0
D) i - j
27. If A = 2i - 5j, what is the unit vector in the direction of A?
A) (2i - 5j) / sqrt(29)
B) (2i + 5j) / sqrt(29)
C) (2i - 5j) / 29
D) (2i - 5j) / 7
28. If A = 3i + 4j, what is the magnitude of vector A?
A) 3
B) 4
C) 5
D) 7
29. In a 3D Cartesian coordinate system, the unit vectors along the positive x, y, and z axes are respectively:
A) j, k, i
B) i, j, k
C) k, i, j
D) i, i, i
30. A unit vector in the direction of a given vector A is represented by:
A) A / |A|
B) A * |A|
C) A / A
D) |A| / A
31. A unit vector is a vector with:
A) Zero magnitude
B) Unit magnitude (magnitude of 1)
C) Infinite magnitude
D) Magnitude equal to the component
32. If A x B = 0 and neither A nor B is a zero vector, then vectors A and B are:
A) Perpendicular
B) Antiparallel
C) Parallel or antiparallel
D) Identical
33. The vector product A x B is generally NOT equal to B x A. Instead, A x B =:
A) B x A
B) -B x A
C) 0
D) 1
34. The vector product of a vector with itself is:
A) The magnitude of the vector
B) The square of the magnitude of the vector
C) Zero vector
D) The vector itself
35. The vector product of two parallel vectors is:
A) Maximum
B) Minimum (zero)
C) Equal to the product of their magnitudes
D) Undefined
36. The vector product (cross product) of two vectors A and B is defined as A x B = |A||B|sin(theta)n, where n is a unit vector perpendicular to the plane containing A and B. This product results in a:
A) Scalar quantity
B) Vector quantity
C) Unit vector
D) Zero vector
37. If A . B = 0 and neither A nor B is a zero vector, then vectors A and B are:
A) Parallel
B) Antiparallel
C) Perpendicular
D) Identical
38. The scalar product of a vector with itself is equal to:
A) Zero
B) The magnitude of the vector
C) The square of the magnitude of the vector
D) The vector itself
39. The scalar product of two perpendicular vectors is:
A) Maximum
B) Minimum (zero)
C) Equal to the product of their magnitudes
D) Undefined
40. The scalar product of two vectors A and B is defined as A . B = |A||B|cos(theta), where theta is the angle between them. This product results in a:
A) Vector quantity
B) Scalar quantity
C) Unit vector
D) Zero vector
41. If two vectors are perpendicular to each other, the angle between them is:
A) 0 degrees
B) 90 degrees
C) 180 degrees
D) 270 degrees
42. The resultant of two vectors A and B, each of magnitude 'a', acting at an angle 'theta' is given by:
A) 2a cos(theta/2)
B) 2a sin(theta/2)
C) 2a cos(theta)
D) 2a sin(theta)
43. When adding two vectors graphically using the head-to-tail method, the resultant vector is drawn from:
A) The tail of the first vector to the head of the second vector
B) The head of the first vector to the tail of the second vector
C) The tail of the second vector to the head of the first vector
D) The head of the second vector to the tail of the first vector
44. The subtraction of two vectors A and B (A - B) is equivalent to:
A) The addition of A and -B
B) The addition of B and -A
C) The addition of A and B
D) The subtraction of B from A
45. If two vectors have the same magnitude and direction, they are considered:
A) Opposite vectors
B) Equal vectors
C) Antiparallel vectors
D) Orthogonal vectors
46. The magnitude of a vector can be:
A) Always positive
B) Always negative
C) Zero or positive
D) Zero or negative
47. Which of the following is NOT a vector quantity?
A) Momentum
B) Work
C) Torque
D) Electric Field
48. A vector quantity is one that possesses:
A) Magnitude only
B) Direction only
C) Both magnitude and direction
D) Neither magnitude nor direction
49. Which of the following is a vector quantity?
A) Mass
B) Time
C) Displacement
D) Temperature
50. Which of the following is a scalar quantity?
A) Velocity
B) Acceleration
C) Speed
D) Force
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