GRADE 11 PHYSICS WORK SHEET-2 VECTORS

MANA BARUMSAA MAKKOO BILLII

MAKKO BILLI SCHOOL
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I. ANSWER THE FOLLOWING QUESTIONS ACCORDINGLY

1. How do you represent a vector graphically?

2. Why do we use of scale diagram in vector drawing?
3. How does vector A differ from vector - A?
4. List types of vectors.
5. If, S = 60km, toward North, write this vector by using a unit vectors.
6. What is the magnitude of unit vector?
7. What is the difference between parallel and anti-parallel vectors?
8. Is that collinear vectors are parallel vectors?
9. Can we say coplanar vectors are perpendicular vectors?
10. The magnitudes of two vectors A and B are 13 units and 9 units, respectively. What are the largest
and smallest possible values for the magnitude of the resultant vector R=A+B?
11. A man rows his boat along the direction of flow of a river (downstream). If the boat can sail in still
water at 0.50 m/s, and the river flows at 0.30 m/s, what is the resultant velocity of the boat?
12. A girl walked across a large field through the following distance in the given order: 72m toward
320 East of North, 57m toward 370 South of West, 18m toward South. Find the magnitude and
direction of the resultant displacement of the girl?
13. A car travels 20km due north and then 25km in a direction 60° West of North. Use both graphical
and algebraic methods to find the magnitude and direction of a single vector that gives the net
effect of the car’s trip.
14. Vector A has x and y components of 4 units and 2 units, respectively and vector B has the
corresponding components of -9 units and 3 units respectively. Find:
(a) The vector components of their resultant.
(b) The magnitude and direction of their resultant.

15. An unknown vector D is added to vector ⃗ = (−4 + 5 ) units and the resultant vector R⃗ = C⃗ +

D⃗ has x and y components of each -1 and 1 units, respectively. Find the magnitude of the unknown
vector.
16. The vector sum P⃗ + Q⃗ is a unit vector along the positive x axis. If P⃗ = ı̂ − ȷ̂ find ⃗

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GRADE 11 PHYSICS WORK SHEET-2
SHEET VECTORS

17. If vector, 0.4ı̂ + bȷ̂ is a unit vector, then what is the value of b?
18. Two vectors give a resultant of magnitude 8 units when are parallel and 2 units when they are
antiparallel. Determine the possible values of each of the vectors.
19. State the condition where the vector sum of two vectors is a null vector.
20. Suppose you are in a large hall and that you mark a point on the floor and start walking the
following distances in the given order: 50 m [forward], 10 m [backward], 10 m [forward], 10 m
[backward], 20 m [forward], 10 m [backward], 40 m [forward], and 10 m [backward].
A. What is the total distance you traveled?
B. What is the magnitude and direction of your displacement from the starting point?
21. What vector must
st be added to vector C of 10km, east in order to give a resultant vector of
A. 15 km, east? B. 15 km, West?
22. A sailor boards a paddle boat and heads the boat Westward directly across a river. The river flows
South at 50 cm/s and the woman paddles
paddle the boat with a speed of 100 cm/s.
A. Determine the resultant velocity of the boat – both magnitude and direction.
B. How far down stream relative to the straight-across
straight across direction will woman be when she reaches
the opposite shore?
23. Given three displacement vectors B, C, and D such that B⃗ = ((−i + 2j)m, C⃗ = (3i −
2jm and D of unknown components, determine the magnitude and direction of for 3B−C+D=0

24. Given displacement vectors of S⃗ and S⃗ as S⃗ = (3i + 6j)m and S⃗ = (−

(−2i − 4j)m find a unit
vector along the direction of S⃗ + S⃗
25. Five displacement vectors A, B, C, D and E are placed on the coordinate axes as shown below. Fill
the following Table with the correct values of the components of the vectors. (Hint: A vector on
either of the coordinate axis has only one component).

26. Displacement vector given as S⃗ =35km, towards 600 North of east. Find the magnitude and
direction of:
a) 1.2S⃗ b) -1.2S⃗

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GRADE 11 PHYSICS WORK SHEET-2 VECTORS

27. Find the angle between each of the pairs of the following vectors:
a) 3ı̂ − ȷ̂ and ı̂ − 2ȷ̂
b) 3ı̂ − 2ȷ̂ and ı̂ − 2ȷ̂
c) 3ı̂ − 2ȷ̂ and 4ı̂ + 6ȷ̂
28.What is the result of scalar or dot product of two vectors?
A. Scalar B. Vector
29.Consider a block placed on a horizontal surface and that force F⃗ is applied on the block to move
the block through displacement ⃗. Find the work done by the force, If F⃗ = (5ı̂ + 3ȷ̂)N and
S⃗ = (−2ı̂ + 4ȷ̂)N ?
30.Consider force F⃗ of a certain machine is applied on a body to move the body with an average
velocity v⃗. if F⃗ = (50ı̂ + 30ȷ̂)N and v⃗ = (3ı̂ + 4ȷ̂)m/s, then find the power developed by the
machine.
31.What is the dot product of vector A⃗ with itself?
32.Show that the dot product of two vectors obeys:
a) Commutative property, A⃗ . B⃗ = B⃗ . A⃗

b) Distributive property, A⃗ . B⃗ + C⃗ = A⃗ . B⃗ + A⃗ . C⃗

33. For what values of the angle between A⃗ and B⃗ will the dot product A⃗ . B⃗, be positive, negative or
zero?
34. If D⃗ = (5ı̂ − 3ȷ̂) and E⃗ = 2ı̂ + j, what is the angle between D⃗ + E⃗ and the x axis?
35. If P⃗ . Q⃗ = PQ, what is the angle between P⃗ and Q⃗ ?
36. What is the dot product of two orthogonal vectors?
37. If A . B⃗ = √ AB, what is the angle between A⃗ and B⃗ ?
38. Write the orthogonality condition of two vectors.
39. What is the dot product of two parallel vectors?

II. CHOOSE THE BEST ANSWER FOR THE FOLLOWING QUESTIONS

40. Which one of the following vector diagrams satisfies the vector equation: ⃗ = ⃗ + ⃗ ?

41. What is the minimum number of vectors of equal magnitudes required to produce a zero resultant?

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GRADE 11 PHYSICS WORK SHEET-2 VECTORS

A. 1 B. 4 C. 2 D. 6
42. A pilot of a tourist plane would like to know a real displacement from Gondar to Harar as shown.
He can determine this displacement between the two tourist attraction sights by calculating:
A. +

B. +

C. −

D. −

43. When two vectors are in the same direction, their sum has:
A. Minimum possible magnitude C. Zero magnitude
B. Maximum possible magnitude D. Undetermined
44. One of the following is NOT vector quantity?
A. magnetic force B. Momentum C. Torque D. Electric potential
45. Suppose A⃗ = 3i − 2j and B⃗ = −i − aj are two vectors in xy-plane. What is the value of a such
that, A⃗ + B⃗ = 2i ?
A. 3 B. 2 C. -2 D. -3
46. If the scalar(dot) product of two vectors is zero, then the two vectors are:
A. Orthogonal B. Parallel C. Anti-parallel D. Zero
47. Vector A and B are perpendicular. Their resultant is 50N, if the value of B=40N, then what is the
value of A?
A. 900N B. 30N C. 70N D. 40N
48. What is the least number of unequal vectors required to produce a zero resultant?
A. 3 B. 5 C. 2 D. 4
49. Given vector P⃗ = 4i + 2j + 6k, if vector Q⃗ is subtracted from it the result is a unit vector along x-
axis. Then what is vector Q⃗ ?
A. 5i + 2j + 6k C. 3i − j + 6k
B. 3i + 2j + 6k D. 3i + j + 6k
50. One of the following is not graphical (geometrical) method of vector addition and subtraction
A. Triangle law C. Polygon law
B. Parallelogram law D. Analytical(algebraic law)
51. Vector A is 2cm long and is 60 above the x-axis in the first quadrant. Vector B is 2cm long 60
below the x-axis in the fourth quadrant. Then, A − B is a vector of magnitude:

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GRADE 11 PHYSICS WORK SHEET-2 VECTORS

A. 2 along +y-axis C. 2 along +x-axis

B. 2√3 along –y-axis D. 2√3 along y-axis
52. If the relation of two vectors are given by A⃗ + B⃗ = 2i + 5j and A⃗ − B⃗ = 4i + 3j, what is the
magnitude of A⃗ ? A. 4 B. 6 C. 5 D. 9
53. Suppose C⃗ = xi + yj + k, which is orthogonal to both vectors A⃗ = i + j − k and B⃗ = −i + j + 2k
then what is vector C⃗ in components?

A. i− j−k C. i − j + k

B. i− j+k D. − i + j − k

54. The resultant of P+Q=13unit, if P=5unit and Q=12unit, what is the angle between A and B?
A. 900 B. 1800 C. 600 D. 00
√
55. If, A⃗ . B⃗ = AB, then what is the angle between vectors A and B?

A. 0° B. 60° C. 30° D. 90°

56. Which pairs of vectors are orthogonal?
2 4 −6 1
A. 4 and −5 C. 4 and 3
6 1 2 5
3 6 1 6
B. 5 and −4 D. −3 and 5
1 2 4 2
57. What is the work done, if a force of (6, −2)N displaced a particle to a position of (3,1)m?
A. 16J B. 18J C. 20J D. 12J
58. If vectors A⃗, B⃗ and C⃗ are non-zero vectors, then which one of the following is TRUE?
A. A⃗ . B⃗ = 0, for A⃗ // B⃗ C. A⃗ . B⃗ = −B⃗ . A⃗
B. A⃗ . B⃗ + C⃗ = A⃗ . B⃗ − A⃗ . C⃗ D. A⃗ . B⃗ + C⃗ = A⃗ . B⃗ + A⃗ . C⃗
59. Two forces of 50N and 80N act upon a body. What are the maximum and minimum possible
values of a resultant respectively?
A. 30N and 40N C. 130N and 30N
B. 30N and 130N D. 40N and 130N
60. If two vectors, A⃗ = 3i − 4j and B⃗ = −4i + 6j and vector C⃗ lies in the xy-plane which is
perpendicular to A⃗. If the dot product of C⃗ and B⃗ is 8. Then what is vector, C⃗ ?
A. 12i + 16j C. 16i − 12j
B. 16i + 12j D. 12i − 16j

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GRADE 11 PHYSICS WORK SHEET-2
SHEET VECTORS

61. The magnitude of two vectors C⃗ and D⃗ are 12 units and 5 units respectively. Which one of the
following is not the possible value for the magnitude of the resultant vector of C and D?
A. 60 units B. 17 units C. 13 units D. 7 units
62. Two non-zero vectors R⃗ and S⃗ are related by R⃗ = cS⃗ where c is a scalar. If the two vectors have
opposite directions, then one of the following is true about c?
A. c is positive number C. c is a negative number
B. c = 1 D. c = 0
63. What is the angle between vectors P⃗ = mi + m√3 j units and Q⃗ = m√3 i + mj units?
A. 90° B. 60°° C. 37° D. 30°
64. Vector A has magnitude of 6 units along the positive x-axis.
x Vector B has magnitude of 4 units and
lies in xy-plane
plane by making an angle of 30° with the positive x-axis.
x axis. Then what is the scalar product
of A and B?
A. 6√3 B. 12√3
12 C. 2√3 D. 88√3
65. Which one of the following is not true about the three vectors?
A. -A = B + C

B. B = -C – A

C. C = -A – B

D. A + B – C = 0

66. Given A⃗ = 3i + 2j + k and B⃗ = 6i + 4j + 2k then which one of the following is true?

A. Both vectors are parallel C. The angle between the two vectors is 30°
B. Both vectors are perpendicular D. The angle between the two vectors is 60°
67. Suppose, P⃗ = (3, −2), Q⃗ = (−1,
( plane with the property P⃗ + Q⃗ −
−4) and R⃗ is vector in the xy-plane
R⃗ = 0,, then which of the following is a unit vector along R⃗ ?

A. 2i − 6j C. i− j
√

B. −2i + 6j D. i− j
√

68. Which method of graphical addition of vectors uses tail to tail techniques in order to find the
resultant of the two vectors?
A. Triangle method B.. Polygon method
metho D. Parallelogram method
hod D. All
By: Habtamu Alemu

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