Line Integrals

Practice Questions

Calculus 3 › Line Integrals

Page 1 of 23

10 of 224

1

Given the vector field

$\vec{F}=yz\vec{i}+xz\vec{j}+xy\vec{k}$

find the divergence of the vector field:

$div \vec{F}$ .

2

Determine if the vector field is conservative or not, and why:

$\left \langle xz, y^2z, z\right \rangle$

3

Find the curl of the vector field:

$\vec{F}=\sec(y)\hat{i}+xy\hat{j}+y^2\hat{k}$

4

Determine if the vector field is conservative or not, and why:

$\left \langle xz, y^2z, z\right \rangle$

5

Find the curl of the vector field:

$\vec{F}=\sec(y)\hat{i}+xy\hat{j}+y^2\hat{k}$

6

Find the curl of the following vector field:

$\vec{F}=\left \langle xy, yz, \cos(z)\right \rangle$

7

Find the curl of the following vector field:

$\vec{F}=\left \langle xy, yz, \cos(z)\right \rangle$

8

Given the vector field

$\vec{F}=yz\vec{i}+xz\vec{j}+xy\vec{k}$

find the divergence of the vector field:

$div \vec{F}$ .

9

Find the divergence of the vector $\left \langle x^2y^2z^2,3y^5,17z\right \rangle$

10

Find the divergence of the vector $\left \langle x^2y^2z^2,3y^5,17z\right \rangle$

Page 1 of 23

Return to subject