Scalars and Vectors. 8. If F x = 11 N and F y = 11 N then the angle between F x and F y is: (a) 30 o (b) 45 o (c) 60 o (d) 90 o
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1 Scalars and Vectors 8. If F x = 11 N and F y = 11 N then the angle between F x and F y is: (a) 30 o (b) 45 o (c) 60 o 90 o 9. If A B o and A x B = o then (a) Either A or B or both are null vectors. (b) A and B are parallel to each other (c) A and B are perpendicular to each other A and B are opposite to each other 10. The product of mass and velocity of a body is called: (a) Torque (b) Force (c) Kinetic energy Momentum 11. Angle O which a vector makes with +x-axis in anticlockwise direction. When its x-component is positive and y-component is negative, will be: (a) 90 o < O < 180 o (b) 180 o < O < 270 o (c) 270 o < O < 360 o 0 o < O < 90 o 12. When dot product of two vectors A and B is zero, then : (a) Either A or B or both are null vectors. (b) A is perpendicular to B (c) A is parallel ; B A and b (e) A and c 13. Magnitude of dot product of two vectors is maximum when: (a) Vectors are of maximum value (b) Vectors are perpendicular to each other (c) Vectors are parallel to each other None of these. 1. When a vector is multiplied by a negative number its direction changes by an angle of: (a) 0 0 (b) 90 0 (c) A vector of magnitude 1 is called: (a) Resultant vector (b) null vector (c) Small vector unit vector 3. Unit vectors are used to specify: (a) Magnitude of a vector (b) Direction of a vector (c) Magnitude as well as direction of a vector Unit of other vectors (e) 4. If A x. A u and A z represent magnitudes of components of a vector A >, then the magnitude of vector A > is given by: (a) A - A x + A u + A z 2 (b) A - A x + A 2 2 u + A z (c) 2 = 5. Law of Cosine used to find: (a) Magnitude of dot product of two vectors (b) Direction of dot product of two vectors (c) Magnitude of resultant of two vectors Direction of resultant of two vectors. 6. Law of Sites can be used to find the: (a) Direction of resultant of two vectors. (b) Magnitude of resultant of two vectors. (c) Magnitude of cross product of two vectors. Direction of cross product of two vectors. 7. is a vector quantity. (a) Mass (b) Distance (c) Torque Work
2 14. According to commutative law: (a) A. B =AB (b) A. B = BA (c) A. B = B. A B. A = BA 15. Dot product of two vectors gives; (a) A scalar quantity (b) A vector quantity (c) A number Sometimes a scalar sometimes a vector quantity = 0 because (a) and are unit vectors (b) and are null vectors (c) and are perpendicular to each other and are parallel to each other 17.. = 1 because: (a) is a unit vector (b) is parallel to (c) is perpendicular to a and b (e) a and c 18. A unit vector parallel to vector is given by: (a) = (b) = (c) =, none of these (19) A -> x B -> = B -> x A -> because: (a) Their magnitude is equal but direction is different (b) Their direction and magnitude both are different (c) Their direction is same but magnitude is different None of the above (20) Unit vector perpendicular to the plane of A -> and B -> is given by: (a) U = (b)u = (b) U = (e) U= 21.Cross product f two vectors give: (a) A scalar quantity (b) A vector quantity (c) A number Sometimes a scalar sometimes a vector quantity. 22. Cross product of two vectors has a maximum value when: (a) The magnitude of vectors is maximum (b) When vectors are parallel to each other. (c) When vectors are perpendicular to each other. 23. Cross product of two vectors and is zero, then. (a) Either or both and are null vectors. (b) is perpendicular to (c) A is parallel to A and B (e) A and c 24. X B is a vector quantity its magnitude is given by: (a) A B Cos (b) A B Sin (c) A B Tan
3 25. x is a vector quantity its direction can be determined by: (a) Head o tail rule (b) Left hand rule (c) Right hand rule Law of Sines 26.. Is a scalar quantity its magnitude is given by? (a) A B Cos (b) A B Sin (c) A B Tan 27. Dot product of vectors obeys: (a) Commutative law (b) Distributive law. (c) Law of Sines. A and B (e) A and C. 28. X = 0 because a) Is a unit vector. b) is parallel to c) is perpendicular to d) A and b. e) A and c 29. X j x = k because: a) and both are unit vector b) and both are unit vectors perpendicular to c) x gives a unit vector perpendicular to d) X gives a unit vector perpendicular to the plane of and. 30. Magnitude of x (a) 1 (b) -1 (c) X is equal to. (a) 1 (b) -1 (c) is an example of dot product of vectors. (a) Acceleration (b) Momentum (c) Torque Power. 33. The resultant of 3 N and 4 N acting perpendicularly on? Body is (a) 1 N (b) 2 N (c) 5 N 7 N 34. Angle between vector and is: (a) 0 o (b) 45 o (c) 90 o 180 o 35. The dot product of two unit vectors perpendicular to one another is: a) 0 (zero) b) 1 c) -1 d) The value of k. ( x ) is: (a) 0 (b) 1 (c)
4 37. If the vector addition of two vectors of magnitude 3 units and 4 units has a resultant of 5 units, then the angle between those two vectors is: (a) 0 o (b) 45 o (c) 90 o 180 o 38. The resultant of two equal and opposite vectors is: (a) A unit vector (b) Null vector (c) Same vector Position vector 39. A force of magnitude 10 N acting on a body produces a displacement of 3 m such that the force and displacement are in opposite direction. Their dot product will be: (a) 30 (b) -30 (c) If cross product of two none zeros vectors is zero then: (a) Vectors are in the same direction. (b) Vectors are perpendicular. (c) Vectors are opposite. Vectors are very small 41. If and are tow vectors then: a). =. b). =. c) x = x 42. If the vector addition of two vectors of magnitude 3 units and 4 units has a resultant of 5 units, then the angle between those two vectors is: (1-b ii, 1996) a) 0 o b) 45 o c) 90 o 43. ( X ) has value: (1 a ii, 2001, 1- a iii, preeng.2002) a) Zero b) One c) d) 44. X is equal to (3-a I pre med 03) a) J 2 b) J c) One d) Zero 45. If a vector quantity is divided by its magnitude the vector obtained is called (1-a iii pre med 03) a) Unit vector b) Position vector c) Null vector d) Free vector 46. The dot product of unit vector & is: (2-a iii pre med 03) a) Zero b) 1 c) -1 d) 47. If = 4i 2j and = 3j, the work done will be (2-a ii pre eng 03) a) 4 joule b) 8 joule c) 2 joule d) 12 joule 48. If. = o when = o, = o the two vectors are 1a ii, 04) a) Parallel b) Opposite c) Perpendicular
5 49. When + =, the angle between the vectors and is: (1a-iii, 04) a) Zero b) 45 o c) 90 o 50. If. = O and x = O and O the vector B is: (1a-ii, 05) a) Equal to b) Zero c) Perpendicular to d) Parallel to 51. The area of a parallelogram formed by two vectors and is given by: (1a-ii, 07) a) ½. ) b) X c) ½ X d). ) 52. Two perpendicular vectors having magnitudes of 4 units and 3 units are added. Their resultant has a magnitude of: (1a-ii, 08) a) 7 units b) 12 units c) 25 units d) 5 units 55. Two perpendicular vectors having magnitudes of 4 units and 3 units are added, their resultant has the magnitude of: (2-xvi, 2009) a) 7 units b) 12 units c) 25 units d) 5 units 56. If. = O and x = O, then vector is: a) Equal to b) Zero c) Perpendicular to d) Parallel to (***** 2010) 57. If. = O and x = O and x O then vector is: 1-vii, 2011) a) Equal to b) Zero c) Perpendicular to d) Parallel to 53. If, and are the unit vectors along x-y and z-axes respectively, then k x j = (2-viii, (a) (b) (c) If a vector is divided by its own magnitude, the resulting vector is called: 2-xi, 2009) a) Position vector b) Unit vector c) Null vector d) Free vector
6 ANSWERS o 2. Unit vector 3. Direction of a vector 4. A = x 2 + A y 2 + A z 2 5. Magnitude of the resultant of two vectors 6. Direction of resultant of two vectors 7. Torque o 9. Either or both are null vectors. 10. Momentum o < 0 < 360 o 12. A and b 13. Vectors are parallel to each other 14.. =. 15. A scalar quantity. 16. And are perpendicular to each other. 17. A and b 18. = / 19. Their magnitude is equal but their direction is different 20. =. X /. x 21. A vector quantity. 22. When vectors are perpendicular. 23. A and c 24. A B Sin Right hand rule 26. A B Cos A and b 28. is perpendicular to 29. x gives a unit vector perpendicular to the plane of and Power N o o 38. Null vector J 40. Vectors are in the same direction. = o 43. One 44. Zero 45. Unit vector 46. Zero Joules 48. Perpendicular o 50. Zero 51. X units Units vector 55. Units 56. Zero 57. Zero.
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