Physics by RD Singh EP

VECTOR
LEVEL-1

1. From fig. , the correct relation is

(a) (b) (c) (d) All of the above

2. Out of the following set of forces, the resultant of which cannot be zero

(a) 10, 10 , 10 (b) 10, 10, 20 (c) 10, 20, 20 (d) 10, 20, 40

3. The resultant of two vectors and is perpendicular to the vector and its magnitude is equal
to half of the magnitude of vector The angle between and is

(a) (b) (c) (d) None of these

4. The ratio of maximum and minimum magnitudes of the resultant of two vectors and is 3:1.
Now , is equal to

(a) (b) 2 (c) 3 (d) 4

5. Two forces , each equal to F , act as shown in fig. Their resultant is

(a) F/2 (b) F

(c) F (d) F
6. Vector is 2 cm long and is above the x –axis in the first quadrant. Vector is 2 cm long and is
below the x-axis in the fourth quadrant. The sum is a vector of magnitude

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Physics by RD Singh EP
(a) 2 cm along positive y – axis (b) 2 cm along positive x-axis
(c) 2cm along negative y – axis (d) 2 cm along negative x - axis
7. If , then the angle between and is
(a) (b) (c) (d)

8. If , and the magnitudes of are 5, 4 , and 3 units, then the angle between
and is

(a) (b) (c) (d)

9. Two vectors and are such that . What is the angle between and ?

(a) (b) (c) (d)

10. Mark the correct statement

(a) (b) (c) (d) All of the above

11. What displacement at an angle to the x-axis has an x-component of 5m ? and are unit
vectors in x and y directions, respectively.
(a) 5 (b) (c) (d) All of the above
12. Out of the following forces, the resultant of which cannot be 10 N?
(a) 15 N and 20 N (b) 10 N and 10 N (c) 5 N and 12 N (d) 12N and 1 N
13. Which of the following pairs of forces cannot be added to give a resultant force of 4 N ?
(a) 2N and 8 N (b) 2 N and 2N (c) 2 N and 6N (d) 2N and 4 N
14. The resultant of the three vectors and shown in fig is

(a) r (b) 2r

(c) (d)

15. The angle between two vectors and is . The resultant of these vectors makes an angle of
with A. Which of the following is true?
(a) A = 2B (b) A = B/2 (c) A = B (d) AB =1
16. A force of 5 N acts on a particle along a direction making an angle of 60° with vertical. Its vertical
component be

(a) 10 N (b) 3 N (c) 4 N (d) 2.5 N

17. There are two force vectors, one of 5 N and other of 12 N at what angle the two vectors be added to
get resultant vector of 17 N, 7 N and 13 N respectively

(a) 0°, 180° and 90° (b) 0°, 90° and 180° (c) 0°, 90° and 90° (d) 180°, 0° and 90°

18. Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the
two forces is

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Physics by RD Singh EP
(a) 45° (b) 120° (c) 150° (d) 60°

19. Forces and act on a point mass in two mutually perpendicular directions. The resultant force
on the point mass will be

(a) (b) (c) (d)

20. Let the angle between two nonzero vectors and be 120° and resultant be

(a) must be equal to (b) must be less than

(c) must be greater than (d) may be equal to

21. For the figure

(a) (b)

(c) (d)

22. Following sets of three forces act on a body. Whose resultant cannot be zero

(a) 10, 10, 10 (b) 10, 10, 20 (c) 10, 20, 23 (d) 10, 20, 40

23. The resultant of two vectors A and B is perpendicular to the vector A and its magnitude is equal to

half the magnitude of vector B. The angle between A and B is

(a) 120° (b) 150° (c) 135° (d) None of these

24. The resultant of two vectors and is If Q is doubled, the new resultant is perpendicular to P.

Then R equals

(a) P (b) (P+Q) (c) Q (d) (P–Q)

25. Given that and that is to . Further if then what is the angle between and

(a) (b) (c) (d)

26. Two equal forces (P each) act at a point inclined to each other at an angle of 120°. The magnitude of
their resultant is

(a) (b) (c) (d) 2P

27. Two forces of 12 N and 8 N act upon a body. The resultant force on the body has maximum value of

(a) 4 N (b) 0 N (c) 20 N (d) 8 N

LEVEL - 2

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Physics by RD Singh EP

28. The projection of a vector on the x-y plane has magnitude

(a) 3 (b) 4 (c) (d)
29. If vector and represent the two sides of a triangle, then the third side of the
triangle can have length equal to
(a) 6 (b) (c) Both of the above (d) None of above

30. Given: =A . A vector , which is perpendicular to , is given by

(a) (b) (c) (d)

31. In going from one city to another, a car travels 75 km north, 60 km north –west and 20 km east.

The magnitude of displacement between the two cities is (take = 0.7)

(a) 170 km (b) 137 km (c) 119 km (d) 140 km

32. The angle which the vector makes with the y-axis , where and are unit vectors along
x- and y – axes, respectively, is

(a) (b) (c) (d) (2/3)

33. A vector when added to the vector = 3 + 4 yields a resultant vector that is in the positive y-
direction and has a magnitude equal to that of . Find the magnitude of .

(a) (b) 10 (c) 5 (d)

34. The vector projection of a vector on y-axis is
(a) 5 (b) 4 (c) 3 (d) Zero
35. If the direction of cosines of the vector are

(a) (b) (c)

(d)

36. A hall has the dimensions A fly starting at one corner ends up at a diametrically
opposite corner. What is the magnitude of its displacement
(a) 17 m (b) 26 m (c) 36 m (d) 20 m
37. The unit vector along is

(a) (b) (c) (d)

38. The angle made by the vector with x- axis is

(a) 90° (b) 45° (c) 22.5° (d) 30°

39. If a unit vector is represented by , then the value of ‘c’ is

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Physics by RD Singh EP
(a) 1 (b) (c) (d)

40. A boy walks uniformally along the sides of a rectangular park of size 400 m× 300 m, starting from
one corner to the other corner diagonally opposite. Which of the following statement is incorrect

(a) He has travelled a distance of 700 m

(b) His displacement is 700 m

(c) His displacement is 500 m

(d) His velocity is not uniform throughout the walk

41. The unit vector parallel to the resultant of the vectors and is

(a) (b) (c) (d)

42. If and then magnitude and direction of will be

(a) (b) (c) (d)

43. If the angle between and is

(a) 60° (b) 0° (c) 120° (d) 90°

44. What vector must be added to the two vectors and so that the resultant may be
a unit vector along x-axis

(a) (b) (c) (d)

45. A body is at rest under the action of three forces, two of which are the third force is

(a) (b) (c) (d)

LEVEL-3
46. The angle between and is

(a) 0 (b) (c) (d)

47. Three vectors satisfy the relation and . The vector is parallel to

(a) (b) (c) (d)

48. Given . Which of the following is perpendicular to ?

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Physics by RD Singh EP
(a) (b) 4 (c) (d)
49. Given and Which of the following is correct?

(a) (b) (c) (d) and are antiparallel

50. If are two non-collinear unit vectors and if , then the value of

is

(a) 2 (b) 3/2 (c) 1/2 (d) 1

51. If then select the correct alternative.

(a) is parallel to

(b) is perpendicular to
(c) Component of along = component of along
(d) component of along = - component of along

52. If a vector is perpendicular to the vector . Then the value of is

(a) –1 (b) (c) (d) 1

53. If then the angle between A and B is

(a)  / 2 (b)  / 3 (c)  (d)

/4

54. Consider two vectors and The magnitude of the scalar product of these
vectors is
(a) 20 (b) 23 (c) (d) 26
55. The angle between the two vectors and will be

(a) Zero (b) 45° (c) 90° (d) 180°

56. The angle between vectors and is

(a) Zero (b)  (c) (d)

57. The resultant of the two vectors having magnitude 2 and 3 is 1. What is their cross product

(a) 6 (b) 3 (c) 1 (d) 0

58. A vector points vertically upward and points towards north. The vector product is
[UPSEAT 2000]
(a) Zero (b) Along west (c) Along east (d) Vertically downward
59. The component of vector along the vector is

(a) (b) (c) (d) 5

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Physics by RD Singh EP

LEVEL-4

60. What is the angle between two vector forces of equal magnitude such that their resultant is one-
third of either of the original forces?

(a) (b) (c) (d)

61. Given and . Find the value of

(a) – 64 (b) 60 (c) - 60 (d) 64

62. Given and If , then the values of p and q are , respectively,

(a) and (b) and (c) and (d) and

63. Choose the wrong statement.

(a) Three vectors of different magnitudes may be combined to give zero resultant.

(b) Two vectors of different magnitudes can be combined to give zero resultant.

(c) the product of a scalar and a vector is a vector quantity.

(d) All of the above are wrong statements.

64. In an equilateral triangle ABC. AL, BM . and CN are medians. Forces along BC and BA represented
by them will have a resultant represented by

(a) 2AL (b) 2BM (c) 2CN (d) AC

65. The vector sum of two forces is perpendicular to their vector difference. The forces are
(a) Equal to each other (b) Equal to each other in magnitude
(c) Not equal to each other in magnitude (d) Cannot be predicted

66. If a parallelogram is formed with two sides represented by vectors and , then represents
the
(a) Major diagonal when the angle between vectors is acute is acute
(b) Minor diagonal when the angle between vectors is obtuse
(c) both of the above
(d) None of the above

67. Two forces due east and =250 N due north have their common initial point.
is

(a) 250 N, (b) 250 N ,

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Physics by RD Singh EP
(c) Zero (d)

68. Two vectors and are at an angle of with each other. Their resultant makes an angle of

with . If = 2 units, then is

(a) (b) (c) (d)

69. The resultant of two vectors and is . If the magnitude of is doubled, the new resultant
vector becomes perpendicular to Then, the magnitude of is equal to

(a) P + Q (b) P (c) P –Q (d) Q

70. ABCDEF is a regular hexagon with point O as centre. The value of is

(a) (b) (c) (d) 0

71. In a two –dimensional motion of a particle, the particle moves from point A, with position vector
, to point B, with position vector . If the magnitudes of these vectors are, respectively,
and and the angles they make with the x=axis are and , respectively, then
find the magnitude of the displacement vector.

(a) 15 (b) (c) 17 (d)

72. The sum of the magnitudes of two forces acting at a point is 16 N. The resultant of these forces is
perpendicular to the smaller force and has a magnitude of 8 N. If the smaller force is of magnitude
x, then the value of x is

(a) 2N (b) 4 N (c) 6 N (d) 7 N

73. The resultant of three vectors 1, 2 and 3 units whose directions are those of the sides of an
equilateral triangle is at an angle of

(a) with the first vector (b) with the first vector

(c) with the first vector (d) with the first vector

74. A unit vector along the incident ray of light is . The unit vector for the corresponding refracted
ray of light is . is a unit vector normal to the boundary of the medium and directed towards the
incident medium. If is the refractive index of the medium, then Snell’s law (second law) of
refraction is

(a) (b) (c) (d)

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Physics by RD Singh EP
75. The components off a vector along the x- and y – directions are (n + 1) and 1, respectively. If the
coordinate system is rotated by an angle , then the components change to n and 3 . The
value of n is

(a) 2 (b) (c) (d) 3.5

76. The distance between the point P (2m, 3m, 4m ) and the x –axis is

(a) m (b) 5 m (c) m (d) m

77. If the angle between the vectors is the value of the product is equal to

(a) (b) (c) (d) zero

78. The sum, difference and cross product of two vectors and are mutually perpendicular if

(a) and are perpendicular to each other and

(b) and are perpendicular to each other

(c) and are perpendicular but their magnitudes are arbitrary

(d) and their direction are arbitrary

79. If , and are the unit vectors along the incident ray, reflected ray and the outward normal to he
reflector. Then

(a) (b) (c) (d)

80. 100 coplanar forces each equal to 10 N act on a body. Each force makes angle with the
preceding force. What is the resultant of the forces
(a) 1000 N (b) 500 N (c) 250 N (d) Zero
81. A truck travelling due north at 20 m/s turns west and travels at the same speed. The change in its
velocity be
(a) 40 m/s N–W (b) m/s N–W (c) 40 m/s S–W (d) m/s S–W
82. If the sum of two unit vectors is a unit vector, then magnitude of difference is
(a) (b) (c) (d)
83. Let then
(a) is always greater then (b) It is possible to have and

(c) C is always equal to A + B (d) C is never equal to A + B

84. The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is
perpendicular to minimum force then the forces are

(a) 6 N and 10 N (b) 8 N and 8 N (c) 4 N and 12 N (d) 2 N and 14 N

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Physics by RD Singh EP
85. Two forces, and are acting on a body. One force is double that of the other force and the
resultant is equal to the greater force. Then the angle between the two forces is

(a) (b) (c) (d)

86. If then which of the following statements is wrong

(a) (b) (c) (d)

87. A vector is along the positive X-axis. If its vector product with another vector is zero then
could be
(a) (b) (c) (d)
88. A body is in equilibrium under the action of three coplanar forces P, Q and R as shown in the figure.
Select the correct statement
Q 
P
(a) (b)  
R

(c) (d)

89. If a body is in equilibrium under a set of non-collinear forces, then the minimum number of forces
has to be

(a) Four (b) Three (c) Two (d) Five

90. As shown in figure the tension in the horizontal cord is 30 N.

A
The weight W and tension in the string OA in Newton are 30o

(a) 30 30 (b) 30 60 30 N
O
(c) 60 30 (d) None of these
W
91. If a vector making angles , , and  respectively with the X, Y and Z axes respectively.
Then
(a) 0 (b) 1 (c) 2 (d) 3
92. If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value
of n is
(a) 1 (b) 2 (c) 3 (d) 4
93. The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is
12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces
(a) 12, 5 (b) 14, 4 (c) 5, 13 (d) 10, 8
94. Figure shows ABCDEF as a regular hexagon. What is the value of
E D
(a)
(b) F C
O
(c)
A B
(d)
95. y component of velocity is 20 and x component of velocity is 10. The direction of motion of the body
with the horizontal at this instant is
(a) (b) (c) 45° (d) 0°

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 Physics by RD Singh EP

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Answers key
(Vector) Physics
1. d b a c a a a a b d d b

2. d b b c d b c b c c b b

3. b c c c a a d a a d b c

4. b d c d d b c a b b a c

5. b a c c c d c a d d c c

6. b c d b b c a a c d a d

7. a c b c b d c b b d d a

8. a d c c b c b b c d a