Deck 3: Additional-Topics-In-Trigonometry

Question 1

Use the vectors , and to find the indicated quantity.State whether the result is a vector or a scalar.
​ ​

A)16; scalar
B) ; vector
C) ; vector
D)22; scalar
E)20; scalar

Answer 1

20; scalar

Question 2

Use the dot product to find the magnitude of u. ​ ​

A)40
B)
C)
D)
E)35

Answer 2

Question 3

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar.
​ ​

A) ; vector
B) ; vector
C) ; vector
D)-240; scalar
E) ; vector

Answer 3

; vector

Question 4

Find the dot product of u and v. ​ ​

A)-31
B)-29
C)-33
D)-37
E)-35

Question 5

Find the dot product of u and v. ​ ​

A)14
B)6
C)12
D)10
E)8

Question 6

Use the vector to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

A) ; vector
B)15; scalar
C)13; scalar
D)11; scalar
E) ; vector

Question 7

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar.
​ ​

A)-96; scalar
B) ; vector
C) ; vector
D) ; vector
E) ; vector

Question 8

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

A) ; vector
B) ; vector
C)-72; scalar
D)60; scalar
E) ; vector

Question 9

Use the dot product to find the magnitude of u. ​ ​

A)
B)
C)
D)
E)

Question 10

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar.
​ ​

A)-1; scalar
B) ; vector
C) ; vector
D)-3; scalar
E)-5; scalar

Question 11

Find the dot product of u and v. ​ ​

A)-41
B)-33
C)-37
D)-35
E)-39

Question 12

Use the dot product to find the magnitude of u. ​
​ ​

A)
B)
C)
D)
E)

Question 13

Use the vectors , to find the indicated quantity.State whether the result is a vector or a scalar. ​ ​

A) ; vector
B)-2; scalar
C)2; scalar
D) ; vector
E)0; scalar

Question 14

Use the vectors , , and to find the indicated quantity.State whether the result is a vector or a scalar.
​ ​

A) ; vector
B) ; vector
C)-58; scalar
D)-56; scalar
E) ; vector

Question 15

Find the dot product of u and v. ​ ​

A)18
B)14
C)20
D)12
E)16

Question 16

Use the dot product to find the magnitude of u. ​ ​

A)
B)
C)
D)
E)

Question 17

Use the dot product to find the magnitude of u. ​ ​

A)5
B)6
C)4
D)7
E)8

Question 18

Find the dot product of u and v. ​ ​

A)-10
B)-8
C)-4
D)-6
E)-2

Question 19

Find the dot product of u and v. ​ ​

A)36
B)40
C)44
D)42
E)38

Question 20

Find the angle between the vectors. ​ ​
(Round the answer to 1 decimal place.)
​

A)
B)
C)
D)
E)

Question 21

Find the angle θ between the vectors. ​
​ ​
(Round the answer to 2 decimal places.)
​

A)
B)
C)
D)
E)

Question 22

Given vectors , and determine whether the result of the following expression is a vector or a scalar. ​

A)vector
B)scalar

Question 23

A force of pounds exerted at an angle of above the horizontal is required to slide a table across a floor (see figure).The table is dragged feet.Determine the work done in sliding the table. ​ ​

A)539.6 ft-lb
B)599.6 ft-lb
C)519.6 ft-lb
D)579.6 ft-lb
E)559.6 ft-lb

Question 24

Find the projection of u onto v.Then write u as the sum of two orthogonal vectors, one of which is .​ ​
​ ​

A)​
B)​
C)​
D)​
E)​

Question 25

Find the angle θ between the vectors. ​
​ ​
(Round the answer to 2 decimal places.)
​

A)
B)
C)
D)
E)

Question 26

Find the projection of u onto v. ​ ​

A)
B)
C)
D)
E)

Question 27

Find the angle θ between the vectors. ​ ​
(Round the answer to 2 decimal places.)
​

A)
B)
C)
D)
E)

Question 28

Find the angle between the vectors u and v if , and Round your answer to two decimal places.

A)1.41°
B)0.00°
C)-1.24°
D)-1.93°
E)0.96°

Question 29

Given and , find .

A)3
B)-3
C)-7
D)9
E)-11

Question 30

A tractor pulls a log 900 meters, and the tension in the cable connecting the tractor and log is approximately 16,691 newtons.The direction of the force is above the horizontal.Approximate the work done in pulling the log. ​
(Round the answer to two decimal places.)
​

A)12,305,260.09 N-m
B)12,305,220.09 N-m
C)12,305,300.09 N-m
D)12,305,280.090 N-m
E)12,305,240.09 N-m

Question 31

Use the dot product to find the magnitude of u if

A)
B)
C)
D)
E)​

Question 32

Determine the work done by a person lifting a 240-newton bag of sugar 2 meters.

A)510 N-m
B)480 N-m
C)520 N-m
D)500 N-m
E)490 N-m

Question 33

Determine the work done by a crane lifting a 2,800-pound car 7 feet.

A)19,600 ft-lb
B)19,620 ft-lb
C)19,610 ft-lb
D)19,640 ft-lb
E)19,630 ft-lb

Question 34

Find the projection of u onto v. ​ ​

A)
B)
C)
D)
E)

Question 35

Find the angle between the vectors u and v if and Round your answer to two decimal places.

A)66.14°
B)68.34°
C)67.38°
D)65.45°
E)68.79°

Question 36

Find the projection of u onto v. ​ ​

A)
B)
C)
D)
E)

Question 37

Given vectors and determine the quantity indicated below.

A)
B)
C)
D)
E)

Question 38

Use the dot product to find the magnitude of u if

A)
B)
C)
D)​
E)

Question 39

Given and , find .

A)-10
B)-14
C)11
D)-5
E)-12

Question 40

Given vectors and determine the quantity indicated below.

A)18
B)-20
C)-22
D)0
E)-6

Question 41

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 6%.

A)$7,664,400
B)$7,791,300
C)$7,918,200
D)$7,723,800
E)$7,768,800

Question 42

Given and , find .

A)0
B)30
C)60
D)61
E)-11

Question 43

Find the angle between the vectors u and v if and Round answer to two decimal places.

A)36.87°
B)37.83°
C)38.28°
D)34.94°
E)35.63°

Question 44

Use vectors to find the measure of the angle at vertex B of triangle ABC, when , , and .Round answer to two decimal places.

A)69.48°
B)71.57°
C)72.91°
D)70.38°
E)74.09°

Question 45

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 6%.

A)​1.06(u + v)
B)1.06
C)
D)1.06
E)1.06

Question 46

Find the angle between the vectors u and v if , and Round answer to two decimal places.

A)167.77°
B)168.46°
C)169.70°
D)170.66°
E)171.11°

Question 47

Determine if , , and where θ is the angle between u and v.Round answer to two decimal places.

A)15.73
B)12.07
C)10.00
D)17.32
E)14.14

Question 48

A 475-pound trailer is sitting on an exit ramp inclined at 32° on Highway 35.How much force is required to keep the trailer from rolling back down the exit ramp? Round your answer to two decimal places.

A)383.93 pounds
B)365.05 pounds
C)402.82 pounds
D)327.27 pounds
E)251.71 pounds

Question 49

Use the dot product to find the magnitude of u if

A)
B)
C)
D)
E)

Question 50

Use the dot product to find the magnitude of u if

A) 10
B)
C)
D)
E)

Question 51

Find the angle between the vectors u and v. ​ ,

A)
B)
C)
D)
E)

Question 52

Given vectors and determine the quantity indicated below.

A)-48
B)-56
C)-46
D)88
E)20

Question 53

Find the projection of u onto v if , . ​

A)​
B)​
C)​
D)​
E)​

Question 54

Determine if , and where θ is the angle between u and v.Round answer to two decimal places.

A)21.21
B)20.49
C)15.00
D)18.11
E)25.98

Question 55

A force of 45 pounds is exerted along a rope attached to a crate at an angle of 30° above the horizontal.The crate is moved 31 feet horizontally.How much work has been accomplished? Round your answer to one decimal place.

A)1,301.6 foot-pounds
B)1,395.0 foot-pounds
C)1,610.8 foot-pounds
D)1,208.1 foot-pounds
E)1,456.2 foot-pounds

Question 56

Use vectors to find the measure of the angle at vertex B of triangle ABC, when , , and .Round answer to two decimal places.

A)95.94°
B)98.47°
C)97.13°
D)95.04°
E)99.65°

Question 57

Given and , find

A)7
B)-5
C)-17
D)11
E)-19

Question 58

Determine whether u are v and orthogonal, parallel, or neither.

A)neither
B)parallel
C)orthogonal

Question 59

Determine whether u are v and orthogonal, parallel, or neither.

A)neither
B)orthogonal
C)parallel

Question 60

Find the angle between the vectors u and v. , ​

A)
B)
C)
D)
E)

Question 61

Find u - v. ​ ​

A)​
B)​
C)​
D)​
E)​

Question 62

Find u - v. ​ ​

A)​-i - 4j
B)-2i - 4j
C)-i + 4j
D)-2i + 4j
E)-i + 5j

Question 63

Find a unit vector in the direction of the given vector. ​
​ ​

A)
B)
C)
D)
E)

Question 64

Find a unit vector in the direction of the given vector. ​ ​

A)​
B)​
C)​
D)
E)​

Question 65

Find a unit vector in the direction of the given vector. ​ ​

A)​
B)​
C)​
D)​
E)

Question 66

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Use dot products to determine the revenue for these two laptops if the price of each is increased by 3.5%.

A)$8,186,667
B)$8,175,000
C)$8,280,000
D)$8,227,500
E)$8,105,000

Question 67

Find the projection of u onto v if ,

A)​
B)​
C)​
D)​
E)​

Question 68

Find u + v. ​ ​

A)​
B) ​
C)​
D)​
E)​

Question 69

Determine whether u are v and orthogonal, parallel, or neither. ,

A)orthogonal
B)parallel
C)neither

Question 70

Find a unit vector in the direction of the given vector. ​ ​

A)j
B)i
C)- j
D)- i
E)​i - j

Question 71

Find u - v. ​ ​

A)​
B)​
C)
D)​
E)​

Question 72

Determine whether u are v and orthogonal, parallel, or neither.

A)orthogonal
B)parallel
C)neither

Question 73

The vector gives the number of units of two models of laptops produced by a company.The vector gives the prices (in dollars) of the two models of laptops, respectively.Identify the vector operation used to increase revenue by 3.5%.

A)
B)
C)
D)
E)

Question 74

Find u + v. ​ ​

A)​
B)
C)​
D)​
E)​

Question 75

Find 2u - 3v. ​ ​

A)
B)​
C)​
D)​
E)​

Question 76

Find a unit vector in the direction of the given vector. ​ ​

A)
B)​
C)​
D)​
E)​

Question 77

46 ​Find the projection of u onto v if , , .

A)​
B)​
C)​
D)​
E)​

Question 78

Find u + v. ​ ​

A)​
B)​
C)​
D)​
E)

Question 79

63​ Find the projection of u onto v if , , .
​

A)​
B)​
C)​
D)​
E)​

Question 80

Find 2u - 3v. ​ ​

A)​
B)
C) ​
D)
E) ​