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13.7 Tangent Planes and Normal Lines 789
13.7 Tangent Planes and Normal Lines
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. For the function given by describe the level surface
given by .
a. sphere of radius 4 centered at the origin
b. circle of radius 4 centered at the origin
c. elliptic cone centered at the origin
d. sphere of radius 16 centered at the origin
e. right circular cone centered at the origin
____ 2. Find the unit normal vector to the surface at the point .
a.
b.
c.
d.
e.
____ 3. Find a unit normal vector to the surface at the point .
a.
b.
c.
790 Chapter 13: Functions of Several Variables
d.
e.
____ 4. Find a unit normal vector to the surface at the point .
a.
b.
c.
d.
e.
____ 5. Find a unit normal vector to the surface at the point .
a.
b.
c.
d.
e.
13.7 Tangent Planes and Normal Lines 791
____ 6. Find an equation of the tangent plane to the surface at the point
.
a.
b.
c.
d.
e.
____ 7. Find an equation of the tangent plane to the surface at the point
.
a.
b.
c.
d.
e.
____ 8. Find an equation of the tangent plane to the surface at the point
.
a.
b.
c.
d.
e.
792 Chapter 13: Functions of Several Variables
____ 9. Find symmetric equations of the normal line to the surface at the
point .
a.
b.
c.
d.
e.
____ 10. Find symmetric equations of the normal line to the surface at the point
.
a.
b.
c.
d.
e.
13.7 Tangent Planes and Normal Lines 793
____ 11. Find symmetric equations of the normal line to the surface at the
point .
a.
b.
c.
d.
e.
____ 12. Find symmetric equations of the tangent line to the curve of intersection of the
surfaces at the point .
a.
b.
c.
d.
e.
794 Chapter 13: Functions of Several Variables
____ 13. Find symmetric equations of the tangent line to the curve of intersection of the
surfaces at the point .
a.
b.
c.
d.
e.
____ 14. Find the angle of inclination of the tangent plane to the surface at
the point . Round your answer to two decimal places.
a.
b.
c.
d.
e.
____ 15. Identify the point(s) on the surface where the tangent
plane is horizontal.
a.
b.
c.
d.
e.
13.7 Tangent Planes and Normal Lines 795
____ 16. Find the point(s) on the hyperboloid where the tangent plane is
perpendicular to the line with parametric equations and .
a.
b.
c.
d.
e.
796 Chapter 13: Functions of Several Variables
13.7 Tangent Planes and Normal Lines
Answer Section
MULTIPLE CHOICE
