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- 1. Multiple-choice20 seconds1 pt
What is the minimum number of vectors with

**unequal**magnitudes whose vector sum can be zero?two

three

four

six

- 2. Multiple-choice20 seconds1 pt
Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by: $A^2$ + $B^2$ = $C^2$ . 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-choice2 minutes1 pt
Given the vector

**A**= 100.00 N at 30.00^{0}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-choice3 minutes1 pt
Three vectors

**A, B**, and**C**have the following*x*and*y*components: A_{x}= 1 m, A_{y}= 0; B_{x}= 1 m, B_{y}= 1 m; C_{x}= 0,C

_{y}= - 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-choice1 minute1 pt
Vectors

**i**,**j**, and**k**are unit vectors directed positively along the x-,y- and z-axes, respectively. The dot product**j**$\cdot$**j**is equal to0

1

**i****k** - 6. Multiple-choice2 minutes1 pt
Two force vectors of magnitudes 21 N and 79 N are added. Which one of the following is the

*only*possible choice of the0 N

28 N

114 N

82 N

- 7. Multiple-choice30 seconds1 pt
The magnitude of a unit vector $\lambda$ is

0

1

-1

2

- 8. Multiple-choice2 minutes1 pt
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-choice3 minutes1 pt
Given: A = 2i - 3j + k, B = i - j + k, C = i - 3j + 2k,

and D = 4i + 2k

The scalar product**D $\cdot$ A**7

11

8

10

- 10. Multiple-choice5 minutes1 pt
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**?47.63

^{0}53.30

^{0}67.82

^{0}112.34

^{0} - 11. Multiple-choice5 minutes1 pt
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-choice30 seconds1 pt
Given:

**A**= 2**i**- 3**j**+**k**The magnitude of

**A**is3.74 units

2 units

1 unit

0

- 13. Multiple-choice10 minutes1 pt
$\cdot$

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**) $\cdot$**C**is0

1

3

5

- 14. Multiple-choice5 minutes1 pt
What are the angles between the force F = 1200i + 800j -1500k and the x-, y-, and z-axes?

$\theta_x$ = $54.78^0$ , $\theta_y$ = $67.39^0$ , $\theta_z$ = $136.13^0$

$\theta_x$ = $54.78^0$ , $\theta_y$ = $67.39^0$ , $\theta_z$ = $43.87^0$

$\theta_x$ = $54.78^0$ , $\theta_y$ = $63.79^0$ , $\theta_z$ = $136.13^0$

$\theta_x$ = $54.78^0$ , $\theta_y$ = $22.71^0$ , $\theta_z$ = $43.78^0$

- 15. Multiple-choice20 seconds1 pt
The ___________ forces do not cause the rotation.

Non-concurrent

Concurrent

Parallel

Non-parallel

- 16. Multiple-choice2 minutes1 pt
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-choice3 minutes1 pt
If

**r**= (**i**+ 2**j**)m and**F**= (10**i**+ 20**j**+ 30**k**)N, then the moment of**F**about the y-axis is0

-30 N-m

67.08 N-m

60 N-m

- 18. Multiple-choice3 minutes1 pt
Refer to the figure, what is the magnitude of the resultant force?

721 N

1,217 N

1,000 N

954 N

- 19. Multiple-choice5 minutes1 pt
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-choice30 seconds1 pt
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-choice3 minutes1 pt
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-choice45 seconds1 pt
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-choice5 minutes1 pt
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-choice45 seconds1 pt
Vector

**A**is 10 m to the right and vector**B**is 8 m to the left. The vector difference**A**-**B**is2 m to the right

2 m to the left

18 m to the right

18 m to the left

- 25. Multiple-choice30 seconds1 pt
Which of the following mathematical statements is

**true**about product of vectors?**A**x**B**=**B**x**A****A**$\cdot$**B**= -(**B $\cdot$ A)****A**x**B**=**A $\cdot$ B****A**x**B**= - (**B**x**A**) - 26. Multiple-choice5 minutes1 pt
Refer to the above figure. The moment of

**F**_{1}zero

15

**k**N-m45

**k**N-m15

**j**N-m - 27. Multiple-choice2 minutes1 pt
Refer to the above figure. The rectangular expression of

**r**is0.60 m

**j**+ 0.50 m**k**0.50 m

**i**+ .60 m**j**0.60 m

**i**+ 0.50 m**j**0.60 m

**i**- 0.50 m**j** - 28. Multiple-choice20 seconds1 pt
Which of the following is

true?*not*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-choice20 seconds1 pt
A body under translational equilibrium

**does not**haveany force acting on it

a velocity

any torque acting on it

a linear acceleration

- 30. Multiple-choice20 seconds1 pt
Two vectors

**A**and**B**have equal magnitudes but opposite in direction. Mathematically, they are related by the equationA = -B

B = -A

**A**=**B****A**= -**B**