**Short Questions**

1. A body of mass ‘’m’’ is moving in the downward direction to an inclined plane making an angle 0 to the horizontal.Find the magnitude of the resultant force?

2. By how many manners the two vectors are multiplied?

3. Can a body be in equilibrium under the action of a single force?

4. Can a body rotate about its center of gravity under the action of its weight?

5. Can a force directed north balance a force directed east?

6. Can a vector have a component greater than the vector’s magnitude?

7. Can the magnitude of a vector have a negative value?

8. Can the magnitude of the resultant of two vectors be greater than the sum of magnitude of individual vector?

9. Can we talk of a vector of zero magnitude?

10. Can you add zero to a null vector?

11. Define null and equal vectors.

12. Define position vector and give its mathematical expression?

13. Define resultant vector?

14. Define static and dynamic equilibrium.

15. Define the term unit vector.

16. Define the Terms: (i)Unit vector (ii) Position vector (iii)Compontents of a vactor?

17. Define torque.

18. Define vector product?

19. Describe two conditions of equilibrium?

20. Differentiate between static and dynamic equilibrium.

21. Differentiate between Transnational and rotational equilibrium?

22. Give an example of a body which is in motion yet is in equilibrium?

23. Give two conditions of equilibrium.

24. Give two example of vector product?

25. How can we find the values of the rectangular components of a vector?

26. How can we subtract the vectors?

27. How would the two vectors of the same magnitude have to be oriented if they were to be combined to given a resultant equal to a vector of the same magnitudes?

28. If all the components of the vector A₁ and A₂ were reversed how would this alter A₁A₂ ?

29. If one of the components of a vector is not zero can its magnitude be zero?

30. If the body is rotating with uniform or constant velocity,What will be the angular velocity and torque acting on the body?

31. Is it possible to add a vector quantity to a scalar quantity?

32. Is it possible to add a vector quantity to a scalar quantity? Explain.

33. Mention the criterion for positive and negative torque.

34. Show that the scalar product of two vectors is commutative?

35. State condition of rotational equilibrium.

36. State Head to Tail Rule of vector addition?

37. State right hand rule to find the direction of resultant of vector product?

38. Suppose the sides of a closed polygon represent vector arranged head to tail.What is the sum of these vectors?

39. The vector so obtained are called the components of the original vectors and the original vector is called the resultant of the components?

40. The vector sum of three vectors gives a zero resultant. What can be the orientation of the vectors?

41. The vector sums of three vectors give a null vector. What can be orientation of the vectors?

42. Two vectors have unequal magnitude. Can their components be equal in magnitude?

43. Two vectors have unequal magnitude. Can their sum be zero? Explain.

44. Two vectors have unequal magnitudes.Can their sum be zero?

45. Under what circumstances would a vector have components that are equal in magnitude?

46. Under what condition the body will be in complete equilibrium?

47. Vector A lies in xy-plane. For what orientation will both of its rectangular components be negative?

48. What are rectangular components of a vector? At what angle there components are equal?

49. What do you understand by positive and negative torques?

50. What is equilibrium?

51. What is negative of A vector?

52. What is resolution of vectors?

53. What is the physical significance of cross product A× B?

54. What is the torque of a force about the point lying on the axis of rotation?

55. What is the torque of force?

56. When a body is in Translational equilibrium

57. Will the value of vector of zero magnitude?

58. With the help of diagram show that A×B = – B×A?

59. Write any two characteristics of vector product.

60. Write down the names of two examples of scalar product?

61. Write two characteristics of scalar product?

62. You are falling off the edge. What should you do to avoid falling?

**Long Questions**

1. Explain vector addition by rectangular components.

2. Define and explain scalar product of vectors and write its characteristics.

3. Define and explain vector product of vectors and write its characteristics. Write down the characteristics of dot and cross product.

4. Define and explain torque

5. Write down the condition for a body a to be on complete equilibrium

6. Suppose, in a rectangular coordinate system, a vector A has its tail at the point P (-2, -3) and its tip at Q (3,9).Deterrnine the distance between these two points. ,

7. A certain corner of a room is selected as” the origin of a rectangular coordinate system. If an insect is sitting on an adjacent wall at’a point having coordinates (2,1), where the units are in metres,.what is the distance of the insect from this corner of the room?

8. What is the unit vector in the direction of the vector A=4 i+3j ?

9. Two particlesare located at r₁ =3i+ 7j and r₂=-2i + 3j respectively. Find both the magnitude of the vector(r₂.r₁) and its orientation with respect to the x-axis.

10. lf a vector B is added to vector A, the result is 6i +j. If B is subtracted from A the result is -4 i +7 j. What ‘is“the‘ magnitude of vector A?

11. Given that A =2i+3j and B =3i-4j, find the magnitude and angle of (a)C=A+B,and (b) D=3A-2B.

12. Find the angle between the two vectors, A =5 i+ j and B =2.i + 4 j

13. Find the work done when the point of application of the force 3i +2j moves in a straight line from the point (2,-1)to the point (6,4).

14. Show that the three vectors i+j+k, 2i -3j + k and 4i+j-5k are mutually perpendicular.

15. Given that A = i-2j+3k and B=3 i-4 k, find the projection of A on B.

16. Vectors A,B and C are 4 units north, 3 units west and 8 units east, respectively. Describe carefully (a) A x B (b) A x C (c) B x C

“17. The torque or turning effect of force about a given point is given by r x F where r is the

vector from the given point to the point of application of F. Consider a force

F = -3i+j+5k (newton) acting on the point 7i+3j+k (m). What is the torque

in N m about the origin?”

18. The line of action of force, F = i -2j, passes through a point whose position vector is (-j+k ). Find (a) the-moment of F about the origin, (b) the moment of F about the point of which the position vector is i +k.

19. The magnitude of dot and cross products of two vectors are 6√3 and 6 respectively. Find the angle between the vectors

20. A load of 10.0 N is suspended from a clothes line. This distorts the line so that it makes an angle of 15° with the horizontal at each end. Find the tension in the clothes line.