Curl

Practice Questions

Calculus 3 › Curl

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1

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

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

2

Find the curl of the vector field:

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

3

Find the curl of the following vector field:

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

4

For the function give the curl of the gradient.

5

Determine the curl of the following vector field:

$\vec{F}=6x\hat{i}+(e^z+y)\hat{j}+z\hat{k}$

6

Evaluate the curl of the force field $F = (x^3+1)\mathbf{i}+xy\mathbf{j}+\ln(z)\mathbf{k}$ .

7

Given that F is a vector function and f is a scalar function, which of the following expressions is undefined?

8

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

$\vec{F}=\left \langle x^2z, xy\cos(y), y^2\right \rangle$

9

Find the curl of the vector field:

$\vec{F}=\left \langle y^2, \sin(x), z\right \rangle$

10

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

$\vec{F}=\left \langle x, y^4e^y, 3z^2\right \rangle$

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