15.1 Vector Fields 901
15.1 Vector Fields
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Sketch the vector field .
a. d.
b. e.
902 Chapter 15: Vector Analysis
c.
____ 2. Sketch several representative vectors in the vector field given by .
a. d.
b. e.
15.1 Vector Fields 903
c.
____ 3. Compute for the vector field given by .
a.
b.
c.
d.
e.
____ 4. Find the gradient vector for the scalar function. (That is, find the conservative vector
field for the potential function.)
a.
b.
c.
d.
e.
904 Chapter 15: Vector Analysis
____ 5. Find the gradient vector for the scalar function. (That is, find the conservative vector
field for the potential function.)
a.
b.
c.
d.
e.
____ 6. Find the conservative vector field for the potential function
by finding its gradient.
a.
b.
c.
d.
e.
15.1 Vector Fields 905
____ 7. Determine whether the vector field is conservative.
a. conservative
b. not conservative
____ 8. Determine whether the vector field is conservative. If it is, find a potential function
for the vector field.
a. conservative with potential function
b. conservative with potential function
c. conservative with potential function
d. conservative with potential function
e. not conservative
____ 9. Determine whether the vector field is conservative. If it is, find a potential function
for the vector field.
a.
conservative with potential function
b.
conservative with potential function
c.
conservative with potential function
d.
conservative with potential function
e. not conservative
906 Chapter 15: Vector Analysis
____ 10. Find the curl for the vector field at the given point.
a.
b.
c.
d.
e.
____ 11. Determine whether the vector field is conservative. If it is, find a potential function
for the vector field.
a. conservative with potential function
b. conservative with potential function
c. conservative with potential function
d. conservative with potential function
e. not conservative
____ 12. Find the divergence of the vector field.
a.
b.
c.
15.1 Vector Fields 907
d.
e.
____ 13. Find the divergence of the vector field F given by
.
a.
b.
c.
d.
e.
____ 14. Find the divergence of the vector field at the given point.
a.
b.
c.
d.
e.
____ 15. Find the divergence at for the vector field
a.
b.
c.
d.
e.
908 Chapter 15: Vector Analysis
____ 16. Find .
a.
b.
c.
d.
e.
____ 17. Find .
a.
b.
c.
d.
15.1 Vector Fields 909
____ 19. Find for the vector field given by
.
a.
b.
c.
d.
e.
____ 18. Find .
a.
b.
c.
d.
e.
910 Chapter 15: Vector Analysis
15.1 Vector Fields
Answer Section
MULTIPLE CHOICE