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MCV4U - Chapter 7: Review Practice
Multiple Choice
The actual Test will be MUCH shorter :)
Note that the amswers are attached at the back. If you have questions about any of the problems, please let me know!
1. A force vector has a magnitude of 14 N and makes an angle of 20 with the x-axis. What is the magnitude of
its horizontal component?
a. 13.16 N c. 14.00 N
b. 4.79 N d. 14.90 N
2. Susan pulls on a rope a sleigh with a force of 120 N. If the rope makes an angle of 25 with the horizontal, what is
the force that tends to lift the sleigh?
a. 120.00 N c. 50.71 N
b. 108.76 N d. 84.85 N
3. Two forces act on an object. The forces have magnitudes of 3 N and 4 N, and act at an angle of 35 to each other.
What is the angle that the resultant makes with the 3 N force?
a. 20.08 c. 35.00
b. 14.91 d. More information is required.
4. A 20 N force acts on an object. The horizontal component of this force has a magnitude of 12 N. What is the angle
the force makes with the horizontal?
a. 53.13 c. 23.58
b. 36.87 d. 66.42
5. An airplane is heading north with an airspeed of 400 km/h. The plane encounters a wind from the east at 100 km/h.
What is the magnitude of the resultant ground velocity?
a. 387 km/h c. 412 km/h
b. 400 km/h d. 500 km/h
−⟶−
− −⟶− −⟶−
⟶
−
6. If a b =8, then what is b a equal to?
1
a. 8 c.
8
b. -8 d. More information is required.
7. If−⟶− ∣−⟶− ∣−⟶− ∣
− ∣9 and 3, what is equal to?
⟶
−
a b = b
a = ∣ ∣
∣ ∣
a. 9 c. 3
b. 81 d. More information is required.
, −⟶− −
8. Under which condition is x 0?⟶
−
y
−⟶− −
a. x ⟶
− are in the same direction.
−⟶−
b. x and −y are perpendicular.
−⟶− ⟶
c. x − are in opposite directions.
and y
−
⟶
−
and y
−⟶− −⟶−
d. None of these conditions force x y to be zero.
9. Two forces of 3N and 8N act on an object at an angle of 30 to each other. What is the dot product of these force
vectors?
a. 4.24 c. 12.00
b. 20.78 d. 24.00
10. Two forces of 4N and 5N act on an object and their corresponding force vectors have a dot product of 8. What is the
angle between the two vectors?
a. 66.42 c. 23.58
b. 27.27 d. 62.73
11. Suppose that−⟶− −⟶− and −⟶− − 2. What is−⟶−equal
−⟶−to?
−⟶−
⟶
3 −
a c = a b
a b
- c =
a. 6 c. -6
b. 2 d. -2
12. Which of the following pairs of vectors are perpendicular to each other?
a. (1, 3, 2) and (- 2, - 6, - 4) c. (4, 14, - 18) and (6, 21, - 27)
b. (13, 4, 2) and (2, - 5, - 3) d. (5, - 4, 3) and (- 3, 4, - 5)
13. For what value of s is the line segment connecting the origin with (3s, ) and the line segment connecting the
origin with (18, 6) perpendicular?
a. 0 c. - 1
b. 1 d. - 9
14. To the nearest degree, what is the angle between the vectors (1, 2, 0) and -(3, 2, 1)?
a. 0 c. 83
b. 42 d. 107
−⟶− −⟶−
15. Given that the vectors a = (6, - 2, 2s) and b = (- 1, s + 1, 2) are perpendicular, what is the value of s?
a. - 4 c. 0
b. - 1 d. 4
−⟶−
−⟶− −⟶− −
16. Given that x ⟶
(1, s, 2s +1) and y (2, 2, 3), for which value of s will x 5?
−
y
a. - 5 c. 1
b. 0 d. 5
−⟶− −⟶−
17. To the nearest degree, what is the angle betweenx = (1, - 3, 4) and y = (- 2, - 2, 3)?
a. 40° c. 63°
MCV4U - Chapter 7: Review Practice
Multiple Choice
The actual Test will be MUCH shorter :)
Note that the amswers are attached at the back. If you have questions about any of the problems, please let me know!
1. A force vector has a magnitude of 14 N and makes an angle of 20 with the x-axis. What is the magnitude of
its horizontal component?
a. 13.16 N c. 14.00 N
b. 4.79 N d. 14.90 N
2. Susan pulls on a rope a sleigh with a force of 120 N. If the rope makes an angle of 25 with the horizontal, what is
the force that tends to lift the sleigh?
a. 120.00 N c. 50.71 N
b. 108.76 N d. 84.85 N
3. Two forces act on an object. The forces have magnitudes of 3 N and 4 N, and act at an angle of 35 to each other.
What is the angle that the resultant makes with the 3 N force?
a. 20.08 c. 35.00
b. 14.91 d. More information is required.
4. A 20 N force acts on an object. The horizontal component of this force has a magnitude of 12 N. What is the angle
the force makes with the horizontal?
a. 53.13 c. 23.58
b. 36.87 d. 66.42
5. An airplane is heading north with an airspeed of 400 km/h. The plane encounters a wind from the east at 100 km/h.
What is the magnitude of the resultant ground velocity?
a. 387 km/h c. 412 km/h
b. 400 km/h d. 500 km/h
−⟶−
− −⟶− −⟶−
⟶
−
6. If a b =8, then what is b a equal to?
1
a. 8 c.
8
b. -8 d. More information is required.
7. If−⟶− ∣−⟶− ∣−⟶− ∣
− ∣9 and 3, what is equal to?
⟶
−
a b = b
a = ∣ ∣
∣ ∣
a. 9 c. 3
b. 81 d. More information is required.
, −⟶− −
8. Under which condition is x 0?⟶
−
y
−⟶− −
a. x ⟶
− are in the same direction.
−⟶−
b. x and −y are perpendicular.
−⟶− ⟶
c. x − are in opposite directions.
and y
−
⟶
−
and y
−⟶− −⟶−
d. None of these conditions force x y to be zero.
9. Two forces of 3N and 8N act on an object at an angle of 30 to each other. What is the dot product of these force
vectors?
a. 4.24 c. 12.00
b. 20.78 d. 24.00
10. Two forces of 4N and 5N act on an object and their corresponding force vectors have a dot product of 8. What is the
angle between the two vectors?
a. 66.42 c. 23.58
b. 27.27 d. 62.73
11. Suppose that−⟶− −⟶− and −⟶− − 2. What is−⟶−equal
−⟶−to?
−⟶−
⟶
3 −
a c = a b
a b
- c =
a. 6 c. -6
b. 2 d. -2
12. Which of the following pairs of vectors are perpendicular to each other?
a. (1, 3, 2) and (- 2, - 6, - 4) c. (4, 14, - 18) and (6, 21, - 27)
b. (13, 4, 2) and (2, - 5, - 3) d. (5, - 4, 3) and (- 3, 4, - 5)
13. For what value of s is the line segment connecting the origin with (3s, ) and the line segment connecting the
origin with (18, 6) perpendicular?
a. 0 c. - 1
b. 1 d. - 9
14. To the nearest degree, what is the angle between the vectors (1, 2, 0) and -(3, 2, 1)?
a. 0 c. 83
b. 42 d. 107
−⟶− −⟶−
15. Given that the vectors a = (6, - 2, 2s) and b = (- 1, s + 1, 2) are perpendicular, what is the value of s?
a. - 4 c. 0
b. - 1 d. 4
−⟶−
−⟶− −⟶− −
16. Given that x ⟶
(1, s, 2s +1) and y (2, 2, 3), for which value of s will x 5?
−
y
a. - 5 c. 1
b. 0 d. 5
−⟶− −⟶−
17. To the nearest degree, what is the angle betweenx = (1, - 3, 4) and y = (- 2, - 2, 3)?
a. 40° c. 63°
