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Chapter 8 Review
1. The vector v has a magnitude of 10 meters and a direction of 92°.
Find the magnitude of its vertical and horizontal components.
1.
2. Find a unit vector u with the same direction as v = ⟨–3, 5⟩.
2.
3. Draw a – 3b for the pair of vectors below by drawing the resultant
vector using the tip to tail method (a free hand drawing is fine).
a
b
3.
4. Find the measure of the angle θ between u = 3i – 4j and v = i + 2j.
𝑎∘𝑏
to the nearest tenth of a degree.
use: 𝑐𝑜𝑠𝜃 = |𝑎||𝑏|
4.
⃑⃑⃑⃑⃑ with initial point
5. Find the component form and magnitude of 𝐴𝐵
A(0, –8) and terminal point B(−1, 7).
5.
6. A force F1 of 27 newtons pulls at an angle of 23° above due east.
A force F2 of 33 newtons pulls at an angle of 55° below due west.
Find the magnitude and direction of the resultant force.
6.
For Questions 7 and 8, find each of the following for
v = ⟨1, −6⟩, w = ⟨2, −5⟩
7. −2v + w
7.
8. 3v + w
8.
⃑⃑⃑⃑⃑ with the give the given initial point A(3,--4)and
9.Write the vector 𝐴𝐵
terminal point B(5,-5) as a linear combination of i and j
9.
For Questions 10 and 11, find each dot product. Then
determine if the vectors are orthogonal.
10.
10. ⟨8, 2⟩ · ⟨0, −6⟩
11. ⟨3, −5,⟩ · ⟨15,7⟩
11.
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Chapter 8 Review
DATE
PERIOD
(continued)
12. A constant force of 15 newtons is being applied at a constant angle of
30° on an object at the same time that a constant force of 25 newtons
at a constant angle of 60° is acting on the object. What is the
magnitude and direction of the resultant force?
13. An airplane is traveling due east with a velocity of 620 miles per hour.
The wind blows at 60 miles per hour at an angle of 50° with the
horizontal. Determine the velocity of the airplane’s flight.
12.
13.
14. FOOTBALL With time running out in a game, Rodney runs with the
football at a speed of 3.8 meters per second and throws the ball at a speed of
7 meters per second at an angle of 28° to the horizontal.
a. Write the component form of the vectors representing Rodney’s velocity
and the path of the ball.
14a.
b. What is the resultant speed and direction of the ball?
14b.
15. Find the projection of u = ⟨7, −2⟩ onto v = ⟨-1,5⟩.
𝑢∘𝑣
Use: 𝑝𝑟𝑜𝑗𝑣 𝑢 = (|𝑣|2 ) 𝑣
15.