Larson_Calculus_10e ch11sec03
MULTIPLE CHOICE
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
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.
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.
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
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
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