← Vector Fields, Divergence & Curl

Practice: Vector Fields

8 multiple choice · 4 free response · 1 walkthroughs

Q1.

basic

Compute

\nabla \cdot F

for

F = ⟨ x^{2}, y^{2}, z^{2} ⟩

.

Q2.

intermediate

Curl of

F = ⟨ y, - x, 0 ⟩

is

Q3.

intermediateLine Integrals T/F #7

True/False: If

\nabla \times F = 0

on a simply connected domain,

F

is conservative.

Q4.

intermediate

\nabla \cdot (\nabla \times F)

equals

Q5.

intermediate

\nabla \times (\nabla f)

equals

Q6.

basic

Is

F = ⟨ y, x ⟩

conservative?

Q7.

intermediateLine Integrals T/F #15

True/False: If

\nabla \cdot F = 0

, then

F

is conservative.

Q8.

basic

\nabla \times F

for

F = ⟨ x, y, z ⟩

is