Question 1

Find the component form and the magnitude of the vector v. Initial Point
Terminal Point
(1, 3)
(-8, -9)

Accepted Answer

A)    
B)    
C) ​   
D) ​   
E) ​   
A)    
B)    
C) ​   
D) ​   
E) ​   C

Question 2

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

Accepted Answer

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

Question 3

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. ​
Initial Point
Terminal Point
(0, -8)
​(9, 12)
​
​

Accepted Answer

A) ​9i + 20j 
B) ​-9i - 20j 
C) ​20i - 9j 
D) ​​20i + 9j 
E) ​9i - 20j 
A) ​9i + 20j 
B) ​-9i - 20j 
C) ​20i - 9j 
D) ​​20i + 9j 
E) ​9i - 20j A

Question 4

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118   , b = 9 and c = 8.
​

Accepted Answer

A) 38.14 sq.units 
B) 31.79 sq.units 
C) 25.43 sq.units 
D) 28.61 sq.units 
E) 34.96 sq.units 
A) 38.14 sq.units 
B) 31.79 sq.units 
C) 25.43 sq.units 
D) 28.61 sq.units 
E) 34.96 sq.units

Question 5

Use the dot product to find the magnitude of u if

Accepted Answer

A)    
B)      
C)    
D) ​     
E)    
A)    
B)      
C)    
D) ​     
E)

Question 6

Find the projection of u onto v. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 7

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

Accepted Answer

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

Question 8

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 50°, b = 4, c = 15
​

Accepted Answer

A) a ≈ 15, B ≈ 13.85°, C ≈ 116.15° 
B) a ≈ 12.80, B ≈ 116.15°, C ≈ 13.85° 
C) a ≈ 4, B ≈ 13.85°, C ≈ 116.15° 
D) a ≈ 15, B ≈ 15.85°, C ≈ 114.15° 
E) a ≈ 12.80, B ≈ 13.85°, C ≈ 116.15° 
A) a ≈ 15, B ≈ 13.85°, C ≈ 116.15° 
B) a ≈ 12.80, B ≈ 116.15°, C ≈ 13.85° 
C) a ≈ 4, B ≈ 13.85°, C ≈ 116.15° 
D) a ≈ 15, B ≈ 15.85°, C ≈ 114.15° 
E) a ≈ 12.80, B ≈ 13.85°, C ≈ 116.15°

Question 9

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

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

Accepted Answer

A) j 
B) i 
C) - j 
D) - i 
E) ​i - j 
A) j 
B) i 
C) - j 
D) - i 
E) ​i - j

Question 11

Given vectors   and   determine the quantity indicated below.

Accepted Answer

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

Question 12

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.

Accepted Answer

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

Question 13

Find the dot product of u and v. ​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

In the figure, α and β are positive angles. ​   ​
A = 9, b = 18
Write α as a function of β.
​

Accepted Answer

A) α = arcsin(9sinβ) 
B) α = sin(   sinβ) ​ 
C) β = arcsin(   sinα) 
D) β = sin(   sinα) 
E) α = arcsin(   sinβ) 
A) α = arcsin(9sinβ) 
B) α = sin(   sinβ) ​ 
C) β = arcsin(   sinα) 
D) β = sin(   sinα) 
E) α = arcsin(   sinβ)

Question 16

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

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

Accepted Answer

A) orthogonal 
B) parallel 
C) neither 
A) orthogonal 
B) parallel 
C) neither

Question 18

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.
​

Accepted Answer

A) 1,812.8 lb 
B) 1,810.8 lb 
C) 1,814.8 lb 
D) 1,811.8 lb 
E) 1,813.8 lb 
A) 1,812.8 lb 
B) 1,810.8 lb 
C) 1,814.8 lb 
D) 1,811.8 lb 
E) 1,813.8 lb

Question 19

Find the magnitude of vector v. ​

Accepted Answer

A)    
B) ​   
C) ​   
D) ​   
E) ​   
A)    
B) ​   
C) ​   
D) ​   
E) ​

Question 20

Given   and   , determine   .

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Find the component form and the magnitude of the vector v. Initial Point Terminal Point (1, 3) (-8, -9)

Use the dot product to find the magnitude of u.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. Initial Point Terminal Point (0, -8) (9, 12)

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118 , b = 9 and c = 8.

Use the dot product to find the magnitude of u if

Find the projection of u onto v.

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

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 50°, b = 4, c = 15

Find the angle between the vectors u and v. ,

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

Given vectors and determine the quantity indicated below.

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.

Find the dot product of u and v.

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

In the figure, α and β are positive angles. A = 9, b = 18 Write α as a function of β.

Find the angle between the vectors u and v. ,

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

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.

Find the magnitude of vector v.

Given and , determine .

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 3: Additional-Topics-In-Trigonometry

Find the component form and the magnitude of the vector v. Initial Point Terminal Point (1, 3) (-8, -9)

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

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. ​ Initial Point Terminal Point (0, -8) ​(9, 12) ​ ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118 , b = 9 and c = 8. ​

Use the dot product to find the magnitude of u if

Find the projection of u onto v. ​ ​

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

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ A = 50°, b = 4, c = 15 ​

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

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

Given vectors and determine the quantity indicated below.

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.

Find the dot product of u and v. ​ ​

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

In the figure, α and β are positive angles. ​ ​ A = 9, b = 18 Write α as a function of β. ​

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

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

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place. ​

Find the magnitude of vector v. ​

Given and , determine .

Trigonometry

Analytic-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Use the dot product to find the magnitude of u.

Select a linear combination of the standard unit vectors i and j of given initial and terminal points of a vector.. Initial Point Terminal Point (0, -8) (9, 12)

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118 , b = 9 and c = 8.

Find the projection of u onto v.

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 50°, b = 4, c = 15

Find the angle between the vectors u and v. ,

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

Find the dot product of u and v.

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

In the figure, α and β are positive angles. A = 9, b = 18 Write α as a function of β.

Find the angle between the vectors u and v. ,

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find W if F = 620 pounds and θ = 20°.Approximate the answer to one decimal place.

Find the magnitude of vector v.