728 Chapter 12: Vector-Valued Functions
12.4 Tangent Vectors and Normal Vectors
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Find the unit tangent vector to the curve given below at the specified point.
a.
b.
c.
d.
e.
____ 2. Find the unit tangent vector to the curve given below at the specified point.
a.
b.
c.
d.
e.
12.4 Tangent Vectors and Normal Vectors 729
____ 3. Find the unit tangent vector for the line tangent to the space curve
at point .
a.
b.
c.
d.
e.
____ 4. Find the principle unit normal vector to the curve given below at the specified point.
a.
b.
c.
d.
e.
730 Chapter 12: Vector-Valued Functions
____ 5. Find the principle unit normal vector to the curve given below at the specified point.
a.
b.
c.
d.
e.
____ 6. Find the principle unit normal vector to the curve given below at the specified point.
a.
b.
c.
d.
e.
12.4 Tangent Vectors and Normal Vectors 731
____ 7. Find at time for the plane curve . Round your answer to three
decimal places.
a. 11.077
b. 7.310
c. 11.797
d. 5.898
e. 5.538
____ 8. Find at time for the plane curve . Round your answer to three
decimal places.
a. 6.581
b. 4.818
c. 3.407
d. 2.154
e. 4.962
____ 9. Find at time for the plane curve . Round your answer to
three decimal places.
a. –40.625
b. –39.209
c. –111.667
d. –46.016
e. –43.988
____ 10. Find at time for the plane curve . Round your answer to
three decimal places.
a. 18.724
b. 23.792
c. 22.264
d. 15.179
e. 22.764
____ 11. Find at time for the space curve . Round your
answer to three decimal places.
a. 0.062
b. 0.071
c. 0.659
d. 0.000
e. 0.753
732 Chapter 12: Vector-Valued Functions
____ 12. Find at time for the space curve .
a. 16
b. 0
c. 5
d. 25
e. 4
____ 13. Find at time for the space curve . Round your
answer to three decimal places.
a. 0.781
b. 0.724
c. 0.343
d. 0.686
e. 0.649
____ 14. Find at time for the space curve . Round your
answer to three decimal places.
a. 0.970
b. 0.465
c. 0.930
d. 1.814
e. 1.060
____ 15. Because of a storm, ground controllers instruct the pilot of a plane flying at an
altitude of 1.6 miles to make a turn and climb to an altitude of 1.8 miles. The model for the path
of the plane during this maneuver is where t is the
time in hours and is the distance in miles. Determine the speed of the plane. Round your answer to
the nearest integer.
a. 50 mi/h
b. 16 mi/h
c. 54 mi/h
d. 34 mi/h
e. 79 mi/h
12.4 Tangent Vectors and Normal Vectors 733
12.4 Tangent Vectors and Normal Vectors
Answer Section