SCALARS AND VECTORS
1. Which of the following is a vector quantity?
a) Time
b) Speed
c) Mass
d) Displacement
2. Two vectors with magnitudes 5 and 8 units, respectively, are added together. What is the minimum possible magnitude of their resultant?
a) 2 units
b) 3 units
c) 8 units
d) 13 units
3. A vector has components of (-3, 4) in the x and y directions, respectively. What is the magnitude of the vector?
a) 3 units
b) 4 units
c) 5 units
d) 7 units
4. The dot product of two vectors is zero. What can you conclude about the vectors?
a) They are parallel.
b) They are perpendicular.
c) They have the same direction.
d) They have the same magnitude.
5. Which of the following is true about the cross product of two vectors?
a) The result is always a scalar.
b) The result is always a vector.
c) The result is always zero.
d) The result depends on the magnitudes of the vectors.
6. A vector has components of (2, -1, 3) in the x, y, and z directions, respectively. What is the angle between the vector and the positive x-axis?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees
7. Two vectors, A and B, have magnitudes 4 and 5 units, respectively. If the angle between them is 60 degrees, what is the magnitude of their vector sum?
a) 1 unit
b) 2 units
c) 3 units
d) 9 units
8. The resultant of two vectors is zero. Which of the following statements is correct?
a) The vectors are parallel.
b) The vectors are perpendicular.
c) The vectors have the same direction.
d) The vectors have the same magnitude.
9. A vector has a magnitude of 6 units and is directed at an angle of 30 degrees above the horizontal. What are the horizontal and vertical components of the vector?
a) 3 units and 5 units
b) 4 units and 3 units
c) 5 units and 3 units
d) 6 units and 3 units
10. Which of the following is a scalar quantity?
a) Force
b) Velocity
c) Temperature
d) Displacement
11. Two vectors with magnitudes 3 and 4 units, respectively, are added together. What is the maximum possible magnitude of their resultant?
a) 1 unit
b) 3 units
c) 4 units
d) 7 units
12. The magnitude of a vector is always:
a) Positive
b) Negative
c) Zero
d) None of the above
13. What is the resultant of adding a vector and its negative?
a) The vector itself
b) Zero vector
c) Negative vector
d) None of the above
14. The cross product of two parallel vectors is:
a) A scalar
b) A vector
c) Zero
d) Undefined
15. A vector has components of (4, 3) in the x and y directions, respectively. What is the angle between the vector and the positive y-axis?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees
16. Two vectors, A and B, have magnitudes 7 and 6 units, respectively. If the angle between them is 90 degrees, what is the magnitude of their vector sum?
a) 1 unit
b) 7 units
c) 13 units
d) 42 units
17. The dot product of two perpendicular vectors is:
a) A scalar
b) A vector
c) Zero
d) Undefined
18. A vector has a magnitude of 5 units and is directed at an angle of 60 degrees above the horizontal. What are the horizontal and vertical components of the vector?
a) 5 units and 5 units
b) 5 units and 2.5 units
c) 2.5 units and 5 units
d) 5 units and 0 units
19. The sum of two vectors has a magnitude equal to the difference of their magnitudes. What can you conclude about the vectors?
a) They are parallel
b) They are perpendicular
c) They have the same direction
d) They have the same magnitude
20. The magnitude of the cross product of two vectors is:
a) A scalar
b) A vector
c) Zero
d) Undefined
21. Which of the following is true about the scalar product (dot product) of two vectors?
a) It is commutative
b) It is associative
c) It results in a vector
d) It is distributive
22. A vector has components of (2, -2, 4) in the x, y, and z directions, respectively. What is the angle between the vector and the positive z-axis?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees
23. Two vectors, A and B, have magnitudes 3 and 5 units, respectively. If the angle between them is 30 degrees, what is the magnitude of their vector difference?
a) 1 unit
b) 2 units
c) 3 units
d) 9 units
24. The cross product of two vectors is maximum when the angle between them is:
a) 0 degrees
b) 45 degrees
c) 90 degrees
d) 180 degrees
25. A vector has components of (3, 4) in the x and y directions, respectively. What is the magnitude of the vector?
a) 3 units
b) 4 units
c) 5 units
d) 7 units
26. The dot product of two vectors is positive. What can you conclude about the angle between the vectors?
a) It is acute
b) It is obtuse
c) It is right angle
d) It is impossible to determine without more information
27. A vector has a magnitude of 6 units and is directed at an angle of 45 degrees above the horizontal. What are the horizontal and vertical components of the vector?
a) 3 units and 3 units
b) 4 units and 4 units
c) 4.24 units and 4.24 units
d) 6 units and 0 units
28. The cross product of two vectors is always perpendicular to:
a) Both of the vectors
b) One of the vectors
c) None of the vectors
d) The plane containing the vectors
29. Which of the following is a valid unit for a vector quantity?
a) Newton
b) Meter
c) Kilogram
d) Meter per second
30. Two vectors are parallel to each other. What can you say about their cross product?
a) It is zero
b) It is a scalar
c) It is undefined
d) It is a vector
31. The cross product of two vectors is minimum when the angle between them is:
a) 0 degrees
b) 45 degrees
c) 90 degrees
d) 180 degrees
32. A vector has components of (1, 2, -3) in the x, y, and z directions, respectively. What is the angle between the vector and the positive x-axis?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees
33. Two vectors, A and B, have magnitudes 4 and 6 units, respectively. If the angle between them is 60 degrees, what is the magnitude of their vector sum?
a) 1 unit
b) 4 units
c) 10 units
d) 12 units
34. The dot product of two vectors is negative. What can you conclude about the angle between the vectors?
a) It is acute
b) It is obtuse
c) It is right angle
d) It is impossible to determine without more information
35. A vector has components of (2, 3) in the x and y directions, respectively. What is the direction of the vector in radians?
a) 0 radians
b) π/4 radians
c) π/3 radians
d) π/2 radians
36. The cross product of two vectors is always parallel to:
a) Both of the vectors
b) One of the vectors
c) None of the vectors
d) The plane containing the vectors
37. Which of the following is a vector quantity?
a) Energy
b) Speed
c) Work
d) Displacement
38. A vector has a magnitude of 7 units and is directed at an angle of 30 degrees below the horizontal. What are the horizontal and vertical components of the vector?
a) 7 units and 3.5 units
b) 7 units and 4 units
c) 3.5 units and 7 units
d) 4 units and 7 units
39. The magnitude of the cross product of two vectors is maximum when the angle between them is:
a) 0 degrees
b) 45 degrees
c) 90 degrees
d) 180 degrees
40. Two vectors are perpendicular to each other. What can you say about their dot product?
a) It is zero
b) It is a scalar
c) It is undefined
d) It is a vector
41. A vector has components of (2, -1, 3) in the x, y, and z directions, respectively. What is the angle between the vector and the positive y-axis?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 90 degrees
42. Two vectors, A and B, have magnitudes 5 and 7 units, respectively. If the angle between them is 120 degrees, what is the magnitude of their vector difference?
a) 1 unit
b) 2 units
c) 3 units
d) 9 units
43. The dot product of two vectors is zero. What can you conclude about the angle between the vectors?
a) It is acute
b) It is obtuse
c) It is right angle
d) It is impossible to determine without more information
44. A vector has components of (-4, 1) in the x and y directions, respectively. What is the direction of the vector in degrees?
a) 30 degrees
b) 45 degrees
c) 150 degrees
d) 180 degrees
45. The cross product of two vectors is always perpendicular to:
a) Both of the vectors
b) One of the vectors
c) None of the vectors
d) The plane containing the vectors
46. Which of the following is a valid unit for a scalar quantity?
a) Newton
b) Meter
c) Kilogram
d) Watt
47. A vector has a magnitude of 8 units and is directed at an angle of 60 degrees above the horizontal. What are the horizontal and vertical components of the vector?
a) 4 units and 4 units
b) 4 units and 6 units
c) 6 units and 4 units
d) 8 units and 0 units
48. Two vectors are parallel to each other. What can you say about their cross-product?
a) It is zero
b) It is a scalar
c) It is undefined
d) It is a vector
49. A vector has components of (-3, 2, 4) in the x, y, and z directions, respectively. What is the angle between the vector and the positive z-axis?
a) 87 degrees
b) 74 degrees
c) 46 degrees
d) 52 degrees
50. The magnitude of the cross product of two vectors is minimum when the angle between them is:
a) 0 degrees
b) 45 degrees
c) 90 degrees
d) 180 degrees
- d) Displacement
- b) 3 units
- c) 5 units
- b) They are perpendicular.
- b) The result is always a vector.
- c) 60 degrees
- d) 9 units
- a) The vectors are parallel.
- c) 5 units and 3 units
- c) Temperature
- d) 7 units
- a) Positive
- b) Zero vector
- c) Zero
- c) 60 degrees
- c) 13 units
- c) Zero
- b) 5 units and 2.5 units
- b) They are perpendicular.
- a) A scalar
- a) It is commutative
- b) 45 degrees
- c) 3 units
- c) 90 degrees
- c) 5 units
- a) It is acute
- b) 4 units and 4 units
- d) The plane containing the vectors
- d) Meter per second
- a) It is zero
- a) 0 degrees
- a) 30 degrees
- c) 10 units
- b) It is obtuse
- c) π/3 radians
- a) Both of the vectors
- b) Speed
- c) 3.5 units and 7 units
- c) 90 degrees
- a) It is zero
- c) 60 degrees
- d) 9 units
- c) It is right angle
- c) 150 degrees
- a) Both of the vectors
- c) Kilogram
- b) 4 units and 6 units
- a) It is zero
- d) 52 degrees
- d) 180 degrees
