Larson_Calculus_10e ch11sec04
MULTIPLE CHOICE
1. Find the cross product of the unit vector .
a.
b.
c.
d.
e.
2. Sketch the graph of the cross product of the unit vector .
a.
d.
b.
e.
c.
3. Given , find .
a.
b.
c.
d.
e.
4. Given and find .
a.
b.
c.
d.
e.
5. Given and find .
a.
b.
c.
d.
e.
6. Given and , find .
a.
b.
c.
d.
e.
7. Given and , find .
a.
b.
c.
d.
e.
8. Find a unit vector that is orthogonal to both and .
a.
b.
c.
d.
e.
9. Find the area of the parallelogram that has the given vectors and as adjacent sides.
a.
b.
c.
d.
e.
10. Find the area of a parallelogram that has the given vectors as adjacent sides. Round your answer to two
decimal places.
a.
b.
c.
d.
e.
11. Find the area of the parallelogram with the vertices , and
. Round your answer to two decimal places.
a.
35.00
b.
3.00
c.
5.92
d.
7.00
e.
2.65
12. Find the area of the triangle with the vertices and . Round
your answer to two decimal places.
a.
20.00
b.
8.00
c.
6.00
d.
2.24
e.
4.47
13. A child applies the brakes on a bicycle by applying a downward force of 25 pounds on the pedal when
the crank makes a angle with the horizontal (see figure). The crank is 6 inches in length. Find the
torque at P. Round your answer to two decimal places.
a.
12.50 ft-lb
b.
6.25 ft-lb
c.
75.00 ft-lb
d.
10.83 ft-lb
e.
21.65 ft-lb
14. Both the magnitude and the direction of the force on a crankshaft change as the crankshaft rotates.
Find the torque on the crankshaft using the position and data shown in the figure. Round your answer
to two decimal places.
a.
2,598.08 ft-lb
b.
259.81 ft-lb
c.
212.13 ft-lb
d.
519.62 ft-lb
e.
150.00 ft-lb
15. Find the triple scalar product .
a.
b.
c.
d.
e.
16. Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by
the vectors
a.
b.
c.
d.
516
e.
17. Find the volume of the parallelepiped with the following vertices.
a.
b.
c.
d.
e.