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Stewart_Calc_7ET ch16sec01
MULTIPLE CHOICE
1. Which plot illustrates the vector field
a.
c.
b.
d.
2. Find the gradient vector field of f.
a.
b.
c.
d.
e.
None of these
3. Match the vector field with its plot.
a.
c.
b.
d.
4. Match the vector field with one of the plots shown below.
a.
c.
b.
d.
5. Find the gradient vector field of the scalar function f. (That is, find the conservative vector
field F for the potential function f of F.)
a.
b.
c.
d.
NUMERIC RESPONSE
1. Find the gradient vector field of
2. The flow lines (or streamlines) of a vector field are the paths followed by a particle whose
velocity field is the given vector field. Thus, the vectors in a vector field are tangent to the
flow lines. The flow lines of the vector field
satisfy the differential equations
and
Solve these differential equations to find the equations of the family of flow lines.
3. Consider the vector field
If a particle starts at the point in the velocity field given by F, find an equation of the
path it follows.
4. Find the gradient vector field of
SHORT ANSWER
1. A particle is moving in a velocity field
At time t = 1 the particle is located at the point (1, 5, 5).
a). What is the velocity of the particle at t = 1?
b). What is the approximate location of the particle at t = 1.01?
