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- 1. Multiple Choice
What is the minimum number of vectors with unequal magnitudes whose vector sum can be zero?
two
three
four
six
- 2. Multiple Choice
Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by: + = . Which statement concerning these vectors is true?
A and B must be at right angles to each other.
They could have any orientation relative to each other.
A and B must have equal lengths.
A and B must be parallel.
- 3. Multiple Choice
Given the vector A = 100.00 N at 30.000 above the negative x- axis. In terms of rectangular form, the vector can also be expressed as
A = -86.60 i + 50.00 j
A = 86.60 i - 50.00 j
A = -50.00 i + 86.60 b j
A = 50.00 i _ 86.60 j
- 4. Multiple Choice
Three vectors A, B, and C have the following x and y components: Ax = 1 m, Ay = 0; Bx = 1 m, By = 1 m; Cx = 0,
Cy = - 1m. According to the graph, how are A, B, and C are combined to give a resultant vector D?
D = A - B - C
D = A - B + C
D = A + B - C
D = A + B + C
- 5. Multiple Choice
Vectors i, j, and k are unit vectors directed positively along the x-,y- and z-axes, respectively. The dot product j j is equal to
0
1
i
k
- 6. Multiple Choice
Two force vectors of magnitudes 21 N and 79 N are added. Which one of the following is the only possible choice of the magnitude of the resultant?
0 N
28 N
114 N
82 N
- 7. Multiple Choice
The magnitude of a unit vector is
0
1
-1
2
- 8. Multiple Choice
Which of the following is not correct?
j x j = 0
j x k = i
j x i = k
j x i = -k
- 9. Multiple Choice
Given: A = 2i - 3j + k, B = i - j + k, C = i - 3j + 2k,
and D = 4i + 2k
The scalar product D A7
11
8
10
- 10. Multiple Choice
Given: A = 2i - 3j + k, B = i - j + k,
C = i - 3j + 2k, and D = 4i + 2k
What is the angle between A and D ?
47.630
53.300
67.820
112.340
- 11. Multiple Choice
Given: A = 2i - 3j + k, B = i - j + k,
C = i - 3j + 2k, and D = 4i + 2k
The vector product between B x C is
- i - j - 2k
i + j + 2k
-i + j + 2k
i - j - 2k
- 12. Multiple Choice
Given: A = 2i - 3j + k
The magnitude of A is
3.74 units
2 units
1 unit
0
- 13. Multiple Choice
Given: A = 2i - 3j + k, B = i - j + k,
C = i - 3j + 2k, and D = 4i + 2k
The scalar triple product of (A x B) C is0
1
3
5
- 14. Multiple Choice
What are the angles between the force F = 1200i + 800j -1500k and the x-, y-, and z-axes?
= , = , =
= , = , =
= , = , =
= , = , =
- 15. Multiple Choice
The ___________ forces do not cause the rotation.
Non-concurrent
Concurrent
Parallel
Non-parallel
- 16. Multiple Choice
In right handed coordinate system which axis is considered to be positive?
The thumb is z-axis, fingers curled from x-axis to y-axis
The thumb is x-axis, fingers is curled from z-axis to y-axis
The thumb is y-axis, fingers curled from x-axis to z-axis
The thumb is z-axis, fingers curled from y-axis to x-axis
- 17. Multiple Choice
If r = (i + 2j)m and F = (10i + 20j + 30k)N, then the moment of F about the y-axis is
0
-30 N-m
67.08 N-m
60 N-m
- 18. Multiple Choice
Refer to the figure, what is the magnitude of the resultant force?
721 N
1,217 N
1,000 N
954 N
- 19. Multiple Choice
Refer to the figure. The moment of the 600 lb about point O is
3,073 ft-lb
4,200 ft-lb
2,400 ft-lb
600 ft-lb
- 20. Multiple Choice
If two vertical ropes are used to support a 20-N weight, the tension in rope must be
20 N
40 N
10 N
30 N
- 21. Multiple Choice
A girl and a boy carry a sack 40 N on a pole between them. If the pole is 6 m long and the load is 2 m from the girl, what force does the boy exerts? Neglect the weight of the pole.
13.3 N
26.7 N
40 N
80 N
- 22. Multiple Choice
A bolt on an engine is to be tighten with a maximum torque of 75 N-m. If a wrench has a length of 0.30 m, what is the maximum force perpendicular to the length that should be used to tighten the bolt?
0.011 N
0.075 N
38 N
250 N
- 23. Multiple Choice
In the figure, the resultant torque about O of the forces acting on a body is
zero
2 N-m counterclockwise
4 N-m counterclockwise
8 N-m clockwise
- 24. Multiple Choice
Vector A is 10 m to the right and vector B is 8 m to the left. The vector difference A - B is
2 m to the right
2 m to the left
18 m to the right
18 m to the left
- 25. Multiple Choice
Which of the following mathematical statements is true about product of vectors?
A x B = B x A
A B = -(B A)
A x B = A B
A x B = - (B x A)
- 26. Multiple Choice
Refer to the above figure. The moment of F1 about point O is
zero
15k N-m
45k N-m
15j N-m
- 27. Multiple Choice
Refer to the above figure. The rectangular expression of r is
0.60 mj + 0.50 mk
0.50 mi + .60 mj
0.60 mi + 0.50 mj
0.60 mi - 0.50 mj
- 28. Multiple Choice
Which of the following is not true?
A moment produced by a force depends on the line of action of the force.
A moment is force times its moment arm
If the vector sum of moments exerted on a body is zero, the body is always in equilibrium.
If the line of action of the the force passes through the axis of rotation, no moment is produced.
- 29. Multiple Choice
A body under translational equilibrium does not have
any force acting on it
a velocity
any torque acting on it
a linear acceleration
- 30. Multiple Choice
Two vectors A and B have equal magnitudes but opposite in direction. Mathematically, they are related by the equation
A = -B
B = -A
A = B
A = -B
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