AnswersPrecalculusDot Product and Work

Dot Product and Work — Unit test Answers

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Which diagram shows the parallelogram method for vector addition?

A
Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the terminal point of vector u, and shares a terminal point with the terminal point of vector v.
Option A
B
Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares a terminal point with the terminal point of vector u, and shares an origin with the terminal point of vector v.
Option B
C
Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right.
Option C
D
Vectors v and u share an origin. Vector v goes up and to the left, and vector u goes down and to the right. Vector u + v shares an origin with the vectors v and u and goes down and to the right and is double the size of vectors v and u.
Option D
2
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Let |u| = 4 at an angle of 210° and |v| = 9 at an angle of 315°, and w = u – v. What is the magnitude and direction angle of w?

A
|w| = 5.5; θ = 156.1°
B
|w| = 5.5; θ = 203.9°
C
|w| = 10.8; θ = 156.1°
D
|w| = 10.8; θ = 203.9°
3

Let u =. What is 3u?

Question illustration
A
LeftAngleBracket 6, 7 RightAngleBracket
Option A
B
LeftAngleBracket 6, 12 RightAngleBracket
Option B
C
LeftAngleBracket 9, 7 RightAngleBracket
Option C
D
LeftAngleBracket 9, 12 RightAngleBracket
Option D
4

Given u = ⟨2, –8⟩ and v = ⟨8, –2⟩, what is u · v?

A
–68
B
–60
C
0
D
32
5

Review the diagram.

Question illustration
A
The horizontal is 150 pounds, and the vertical is 260 pounds.
B
The horizontal is 260 pounds, and the vertical is 150 pounds.
C
The horizontal is 346 pounds, and the vertical is 600 pounds.
D
The horizontal is 600 pounds, and the vertical is 346 pounds.
6

A vector has initial point at (3, –5) and terminal point at (–2, 3). What are the characteristics of this vector?

A
The magnitude is , and the direction angle is about 58°.
Option A
B
The magnitude is , and the direction angle is about 122°.
Option B
C
The magnitude is , and the direction angle is about 58°.
Option C
D
The magnitude is , and the direction angle is about 122°.
Option D
7

A force of 50 pounds acts in a direction 60° above horizontal, moving an object 100 feet from (0, 0) to (100, 0). How much work is done by the force?

A
25 foot-pounds
B
50 foot-pounds
C
2,500 foot-pounds
D
5,000 foot-pounds
8

A boat leaves a pier and travels 15 miles due east, then turns and travels 15 miles in the direction N 20° E. Which diagram represents the boat’s current distance, x, from the pier?

A
On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with a vertical line and vector 15 miles is 20 degrees.
Option A
B
On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the right. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed with the x-axis and vector 15 miles is 20 degrees.
Option B
C
On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by a vertical line and vector 15 miles is 20 degrees.
Option C
D
On a coordinate plane, a vector labeled 15 miles is on the x-axis. From that vector, another vector labeled 15 miles goes up and to the left. Vector x goes from (0, 0) to the terminal point of vector 15 miles. Angle a formed by vector 15 miles and the x-axis is 20 degrees.
Option D
9

Review the graph.

Question illustration
A
magnitude of and direction angle equal to approximately 40°
Option A
B
magnitude of and direction angle equal to approximately 50°
Option B
C
magnitude of and direction angle equal to approximately 40°
Option C
D
magnitude of and direction angle equal to approximately 50°
Option D
10

The speed of a boat in still water is 25 mph. The boat is traveling on a river with a current flowing south at 10 mph. At what angle upstream should the boat head to travel due west?

A
21.80°
B
23.58°
C
66.42°
D
68.20°
11

Let |r| = 6 at an angle of 30° and |s| = 11 at an angle of 225°. Which expression represents |r – s|?

A
StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (15 degrees) EndRoot
Option A
B
StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (45 degrees) EndRoot
Option B
C
StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (165 degrees) EndRoot
Option C
D
StartRoot 6 squared + 11 squared minus 2 (6) (11) cosine (255 degrees) EndRoot
Option D
12

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components . After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station.What are the characteristics of the vector representing the path of the ship?

Question illustration
A
components:, magnitude: 13.46
Option A
B
components:, magnitude: 53.85
Option B
C
components:, magnitude: 13.46
Option C
D
components:, magnitude: 53.85
Option D
13

Let a = 2i + 9j, b = –4i + 5j, c = i – 3j, and d = 14j where i and j are unit vectors. What is (a – b) – (2d – c) in terms of i and j?

A
5i – 27j
B
5i + 35j
C
7i – 27j
D
7i + 39j
14

Review the graph.

Question illustration
A
(StartFraction 25 Over 2 EndFraction, StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)
Option A
B
(StartFraction 25 Over 2 EndFraction, negative StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)
Option B
C
(negative StartFraction 25 Over 2 EndFraction, StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)
Option C
D
(negative StartFraction 25 Over 2 EndFraction, negative StartFraction 25 StartRoot 3 EndRoot Over 2 EndFraction)
Option D
15

The magnitude of vector u is 34, and the magnitude of vector v is 20. The dot product u · v = –10. What is the approximate angle between the vectors?

A
79°
B
89°
C
91°
D
101°
16

Given vectors u = ⟨–2, 3⟩ and v = ⟨–6, 9⟩, what is the measure of the angle between u and v?

A
0°
B
86°
C
91°
D
180°
17

Given u = ⟨3, 2⟩, v = ⟨1, 5⟩, and the angle between the vectors is 45°, what is u · v?

A
3
B
4
C
13
D
21
18

For the vectors u = ⟨2, 9⟩, v = ⟨4, –8⟩, and w = ⟨–12, 4⟩, what is u + v + w?

A
⟨6, 1⟩
B
⟨6, 5⟩
C
⟨-6, 5⟩
D
⟨-6, 21⟩
19

Review the graph.

Question illustration
A
13.23 pounds
B
38.78 pounds
C
43.95 pounds
D
53.23 pounds
20

Given vectors u and v, with |u| = 10 and |v| = 12, and the angle between the vectors is 53°, what is u · v?

A
0.72
B
1.20
C
13.24
D
72.22

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