NEET UG - Scalars and vectors, vector addition and subtraction, scalar and vector products, unit vector Online Test (MCQ Quiz)

1. Which of the following is a scalar quantity?

A) Velocity B) Acceleration C) Speed D) Force

2. Which of the following is a vector quantity?

A) Mass B) Time C) Displacement D) Temperature

3. A vector quantity is one that possesses:

A) Magnitude only B) Direction only C) Both magnitude and direction D) Neither magnitude nor direction

4. Which of the following is NOT a vector quantity?

A) Momentum B) Work C) Torque D) Electric Field

5. The magnitude of a vector can be:

A) Always positive B) Always negative C) Zero or positive D) Zero or negative

6. If two vectors have the same magnitude and direction, they are considered:

A) Opposite vectors B) Equal vectors C) Antiparallel vectors D) Orthogonal vectors

7. 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

8. 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

9. 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)

10. 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

11. 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

12. The scalar product of two perpendicular vectors is:

A) Maximum B) Minimum (zero) C) Equal to the product of their magnitudes D) Undefined

13. 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

14. 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

15. 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

16. The vector product of two parallel vectors is:

A) Maximum B) Minimum (zero) C) Equal to the product of their magnitudes D) Undefined

17. 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

18. 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

19. 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

20. 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

21. 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

22. 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

23. If A = 3i + 4j, what is the magnitude of vector A?

A) 3 B) 4 C) 5 D) 7

24. 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

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. Let A = 2i + 3j and B = 4i - j. What is A . B?

A) 5 B) -5 C) 11 D) 10

28. 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

29. The angle between vector A = i and vector B = j is:

A) 0 degrees B) 45 degrees C) 90 degrees D) 180 degrees

30. The angle between vector A = i and vector B = -i is:

A) 0 degrees B) 90 degrees C) 180 degrees D) 270 degrees

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. The direction of a vector can be indicated by:

A) Its length B) An arrow head C) Its magnitude D) Its sign

38. 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

39. 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

40. If A = 5i and B = 2j, what is the magnitude of A x B?

A) 0 B) 7 C) 10 D) 10k

41. If A = 5i and B = 2i, what is the magnitude of A x B?

A) 0 B) 7 C) 10 D) 10i

42. 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

43. 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

44. If A = 2i + 3j and B = -3i - 2j, what is the scalar product A . B?

A) 0 B) -12 C) 13 D) -13

45. If A = 2i + 3j and B = -3i - 2j, what is the magnitude of A+B?

A) 0 B) 1 C) sqrt(2) D) 2

46. 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

47. 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

48. If a vector has components Ax = 5 and Ay = -12, its magnitude is:

A) 5 B) 12 C) 13 D) 17

49. 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|

50. 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

Scalars and vectors, vector addition and subtraction, scalar and vector products, unit vector - Online Test

Test Results