Class 11 Physics Chapter 2 – Vectors MCQs - MCQs

Description: Practice Class 11 Physics Chapter 2 Vectors MCQs according to the FBISE HSSC-I syllabus. These exam-oriented questions cover vector representation, unit vectors, components, vector addition, scalar product, vector product, projections, work, and scalar triple product.

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1. A vector quantity has

A. magnitude onlyB. direction onlyC. both magnitude and directionD. neither magnitude nor direction

2. Which of the following is a scalar quantity?

A. displacementB. velocityC. forceD. mass

3. Which of the following is a vector quantity?

A. speedB. distanceC. temperatureD. displacement

4. A unit vector has magnitude

A. 0B. 1C. -1D. 10

5. The standard unit vectors along the x, y and z axes are

A. i, j, kB. x, y, zC. a, b, cD. p, q, r

6. The magnitude of $\mathbf{A}=3\mathbf{i}+4\mathbf{j}$ is

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

7. The magnitude of $\mathbf{A}=2\mathbf{i}-3\mathbf{j}+6\mathbf{k}$ is

A. 7B. $\sqrt{13}$ C. $\sqrt{45}$ D. 11

8. The rectangular components of a vector are along

A. mutually perpendicular axesB. the same line onlyC. no directionD. zero-magnitude axes

9. If a vector A makes angle θ with the positive x-axis, its x-component is

A. $A\sin\theta$ B. $A\cos\theta$ C. $A\tan\theta$ D. $A/\cos\theta$

10. Its y-component is

A. $A\cos\theta$ B. $A\tan\theta$ C. $A\sin\theta$ D. $A/\sin\theta$

11. A vector of magnitude 10 at 30° to x-axis has x-component

A. 5B. $5\sqrt3$ C. $10\sqrt3$ D. 20

12. The same vector has y-component

A. 5B. $5\sqrt3$ C. $10\sqrt3$ D. 20

13. Two vectors are equal if they have

A. equal magnitudes onlyB. same direction onlyC. same magnitude and same directionD. opposite directions

14. Two vectors are parallel if they have

A. the same or opposite directionB. equal magnitudes onlyC. zero magnitudesD. perpendicular directions

15. The negative of a vector has

A. same magnitude and opposite directionB. opposite magnitude and same directionC. zero magnitudeD. double magnitude

16. Vector addition obeys the

A. commutative lawB. inverse-square lawC. Ohm’s lawD. law of reflection

17. If two vectors of magnitudes A and B act in the same direction, resultant magnitude is

A. A-BB. |A-B|C. A+BD. $\sqrt{A^2+B^2}$

18. If two equal vectors act in opposite directions, their resultant is

A. twice either vectorB. one vectorC. zeroD. infinite

19. For perpendicular vectors of magnitudes 3 and 4, the resultant magnitude is

A. 1B. 5C. 7D. 12

20. The magnitude of the resultant of A and B with angle θ between them is

A. $\sqrt{A^2+B^2+2AB\cos\theta}$ B. $A+B\cos\theta$ C. A-BD. $AB\sin\theta$

21. If two vectors are perpendicular, their dot product is

A. 1B. -1C. zeroD. maximum

22. The scalar product of A and B is

A. $AB\sin\theta$ B. $AB\cos\theta$ C. A/BD. A+B

23. The dot product $\mathbf{i}\cdot\mathbf{j}$ is

A. 1B. -1C. 0D. k

24. The dot product $\mathbf{i}\cdot\mathbf{i}$ is

A. 0B. 1C. -1D. i

25. If $\mathbf{A}=2\mathbf{i}+3\mathbf{j}$ and $\mathbf{B}=4\mathbf{i}-\mathbf{j}$ , then A·B is

A. 5B. 8C. 11D. 14

26. Two non-zero vectors are perpendicular if their dot product is

A. 1B. -1C. 0D. AB

27. Work done by constant force F through displacement s is

A. $Fs\sin\theta$ B. $Fs\cos\theta$ C. F/sD. F+s

28. If force and displacement are perpendicular, work done is

A. maximumB. zeroC. negative infinityD. equal to force

29. The vector product A × B is

A. a scalarB. a vector perpendicular to bothC. always zeroD. a unit vector

30. The magnitude of the cross product is

A. $AB\cos\theta$ B. $AB\sin\theta$ C. A+BD. A-B

31. The cross product of parallel vectors is

A. maximumB. zeroC. oneD. undefined

32. $\mathbf{i}\times\mathbf{j}$ equals

A. iB. jC. kD. -k

33. $\mathbf{j}\times\mathbf{k}$ equals

A. iB. -iC. jD. k

34. $\mathbf{k}\times\mathbf{i}$ equals

A. -jB. jC. iD. -i

35. Unlike the dot product, the cross product is

A. commutativeB. anti-commutativeC. always scalarD. always zero

36. The angle between two non-zero vectors can be found from

A. $\cos\theta=\frac{\mathbf{A}\cdot\mathbf{B}}{AB}$ B. $\sin\theta=\frac{A+B}{AB}$ C. $\tan\theta=A+B$ D. $\cos\theta=AB$

37. The projection of A on the direction of B is

A. $A\sin\theta$ B. $A\cos\theta$ C. ABD. A+B

38. If A·B > 0, the angle between them is

A. acuteB. rightC. obtuseD. straight only

39. If A·B < 0, the angle between them is

A. acuteB. rightC. obtuseD. zero

40. The scalar triple product is written as

A. $\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})$ B. $\mathbf{A}\times(\mathbf{B}\times\mathbf{C})$ C. A+B+CD. ABC

41. The scalar triple product gives

A. a scalarB. a vector onlyC. an angle onlyD. a unit vector

42. The absolute value of a scalar triple product represents the volume of a

A. circleB. parallelogramC. parallelepipedD. line

43. Three vectors are coplanar if their scalar triple product is

A. 1B. -1C. zeroD. maximum

44. The volume of a parallelepiped formed by A, B and C is

A. A+B+CB. $|\mathbf{A}\cdot(\mathbf{B}\times\mathbf{C})|$ C. $AB\cos C$ D. ABC only

45. If $\mathbf{A}=2\mathbf{i}+\mathbf{j}$ and $\mathbf{B}=\mathbf{i}-2\mathbf{j}$ , then A·B is

A. 0B. 2C. 4D. -4

46. A force of 10 N moves an object 2 m in the same direction. Work done is

A. 5 JB. 12 JC. 20 JD. 100 J

47. If A = 3i + 4j, a unit vector in the direction of A is

A. 3i+4jB. $\frac35\mathbf{i}+\frac45\mathbf{j}$ C. $\frac43\mathbf{i}+\frac34\mathbf{j}$ D. 5i+5j

48. A vector with components 6 and 8 has magnitude

A. 10B. 14C. 48D. 100

49. If $\mathbf{A}=3\mathbf{i}+4\mathbf{j}$ and $\mathbf{B}=3\mathbf{i}+4\mathbf{j}$ , then $|A+B|$ is

A. 5B. 10C. 7D. 25

50. If two vectors have magnitudes 5 and 5 and are perpendicular, their resultant magnitude is

A. 5B. $5\sqrt2$ C. 10D. 25

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Syllabus & SLO Alignment

FBISE syllabus: National Curriculum of Pakistan 2022–23, FBISE Assessment Framework for Physics Grade XI.

Content area: Domain B – Mechanics

Relevant SLOs: P-11-B-01 to P-11-B-02

Alignment: Representation of vectors in components; scalar (dot) and vector (cross) products and their properties.

Assessment note: The FBISE framework distinguishes summative SLOs used in the final examination from formative SLOs used in teaching-learning. MCQs on this page should be treated as practice aligned to the listed content/SLOs, not as a reproduction of the official FBISE paper.

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