Deck 11: Section 3: Vectors and the Geometry of Space

Question 1

Suppose a 48000-pound truck is parked on a slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force perpendicular to the hill. Round your answer to one decimal place.

A) 47,008.8 lb
B) 47,426.8 lb
C) 47,328.8 lb
D) 47,270.8 lb
E) 47,289.8 lb

Answer 1

47,270.8 lb

Question 2

Determine whether u and v are orthogonal, parallel and pointing in the same direction, parallel and pointing in opposite directions, or neither.

A) Orthogonal
B) Parallel, opposite direction
C) Parallel, same direction
D) Neither parallel nor orthogonal

Answer 2

Neither parallel nor orthogonal

Question 3

Given and , find the vector component of u orthogonal to v.

A)
B)
C)
D)
E)

Answer 3

Question 4

Given and find .

A)
B)
C)
D)
E)

Question 5

Find the angle between the vectors for u and v given below.

A)
B)
C)
D)
E)

Question 6

Find the direction angles of the vector u given below. Round your answer to one decimal place.

A)
B)
C)
D)
E)

Question 7

An object is pulled 5 feet horizontally across a floor, using a force of 95 pounds. The direction of the force is above the horizontal. Find the work done. Round your answer to two decimal places.

A) 467.78 ft-lb
B) 398.56 ft-lb
C) 82.48 ft-lb
D) 6.96 ft-lb
E) 511.94 ft-lb

Question 8

Suppose the vector gives the numbers of hamburgers, chicken sandwiches, and cheeseburgers, respectively, sold at a fast-food restaurant in one week. The vector gives the prices (in dollars) per unit for the three food items. Determine the total revenue that the restaurant earned on its three products for that week. Round your answer to two decimal places.

A) $12,079.58
B) $12,118.58
C) $24,138.16
D) $12,068.58
E) $24,136.16

Question 9

Given , find .

A) -6
B) 12
C) -8
D) -2
E) 20

Question 10

Find the angle between the vectors for u and v.

A) 8.13
B) 89.77
C) 81.87
D) 8.05
E) 12.33

Question 11

Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a angle with the horizontal. Find the work done in towing the car 4 kilometers. Round your answer to two decimal places.

A) 9,426.60 km-N
B) 4,712.80 km-N
C) 4,726.80 km-N
D) 9,424.60 km-N
E) 2,197.61 km-N

Question 12

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

A) Parallel, same direction
B) Orthogonal
C) Neither parallel nor orthogonal
D) Parallel, opposite direction

Question 13

Suppose a toy wagon is pulled by exerting a force of 25 pounds on a handle that makes a angle with the horizontal as shown in the figure below. Find the work done in pulling the wagon 50 feet. Round your answer to one decimal place.

A) 1,200.0 ft-lb
B) 427.5 ft-lb
C) 2,350.2 ft-lb
D) 1,174.6 ft-lb
E) 2,348.2 ft-lb

Question 14

Find the direction cosines of the vector u given below.

A)
B)
C)
D)
E)

Question 15

Suppose a 58000-pound truck is parked on a slope as shown in the figure. Assume the only force to overcome is that due to gravity. Find the force required to keep the truck from rolling down the hill. Round your answer to two decimal places.

A) 29,000.00 lb
B) 28,615.00 lb
C) 29,135.00 lb
D) 29,056.00 lb
E) 29,011.00 lb

Question 16

Given and find .

A) -8
B) -4
C) 4
D) 7
E) -1

Question 17

Find the direction cosines of the vector u given below.

A)
B)
C)
D)
E)

Question 18

Given and , find the projection of u onto v.

A)
B)
C)
D)
E)