Multivariable Calculus Quiz
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VECTOR FIELDS
Question 1
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A vector field is given by
F
⃗
(
x
,
y
)
=
⟨
2
y
,
−
x
⟩
\vec{F}(x,y) = \langle 2y, -x \rangle
F
(
x
,
y
)
=
⟨
2
y
,
−
x
⟩
. Which of the following parameterized curves
r
⃗
(
t
)
\vec{r}(t)
r
(
t
)
corresponds to a field line of
F
⃗
\vec{F}
F
?
A
r
⃗
(
t
)
=
⟨
cos
(
t
)
,
sin
(
t
)
⟩
\vec{r}(t) = \langle \cos(t), \sin(t) \rangle
r
(
t
)
=
⟨
cos
(
t
)
,
sin
(
t
)⟩
B
r
⃗
(
t
)
=
⟨
cos
(
2
t
)
,
sin
(
2
t
)
⟩
\vec{r}(t) = \langle \cos(2t), \sin(2t) \rangle
r
(
t
)
=
⟨
cos
(
2
t
)
,
sin
(
2
t
)⟩
C
r
⃗
(
t
)
=
⟨
2
cos
(
2
t
)
,
sin
(
2
t
)
⟩
\vec{r}(t) = \langle \sqrt{2}\cos(\sqrt{2}t), \sin(\sqrt{2}t) \rangle
r
(
t
)
=
⟨
2
cos
(
2
t
)
,
sin
(
2
t
)⟩
D
r
⃗
(
t
)
=
⟨
e
2
t
,
e
−
2
t
⟩
\vec{r}(t) = \langle e^{\sqrt{2}t}, e^{-\sqrt{2}t} \rangle
r
(
t
)
=
⟨
e
2
t
,
e
−
2
t
⟩
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