664 Chapter 11: Vectors and the Geometry of Space
11.3 The Dot Product of Two Vectors
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Given
and find .
a. –8
b. –4
c. 4
d. 7
e. –1
____ 2. Given , find .
a. –6
b. 12
c. –8
d. –2
e. 20
____ 3. Given and find .
a.
b.
c.
d.
e.
____ 4. Find the angle between the vectors for u and v given below.
a.
b.
c.
d.
e.
____ 5. Find the angle between the vectors for u and v.
a. 48.22
b. 2.73
c. 87.27
d. 44.97
e. 88.64
11.3 The Dot Product of Two Vectors 665
____ 6. 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
____ 7. 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
____ 8. Find the direction cosines of the vector u given below.
a.
b.
c.
d.
e.
666 Chapter 11: Vectors and the Geometry of Space
____ 9. Find the direction cosines of the vector u given below.
a.
b.
c.
d.
e.
____ 10. Find the direction angles of the vector u given below. Round your answer to one
decimal place.
a.
b.
c.
d.
e.
____ 11. Given and , find the projection of u onto v.
a.
b.
c.
d.
e.
____ 12. Given and , find the vector component of u orthogonal to v.
a.
b.
c.
d.
e.
11.3 The Dot Product of Two Vectors 667
____ 13. 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
____ 14. 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
668 Chapter 11: Vectors and the Geometry of Space
____ 15. 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
____ 16. 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
11.3 The Dot Product of Two Vectors 669
____ 17. 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
____ 18. 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
670 Chapter 11: Vectors and the Geometry of Space
11.3 The Dot Product of Two Vectors
Answer Section