14.5 - Divergence and Curl Practice

 $\nabla\times\left(\nabla\cdot\overrightarrow{F}\right)$  
What will this operation result in?

• Scalar function

• Vector function

• Undefined

 $\nabla\cdot\left(\nabla\times\overrightarrow{F}\right)$  
What will this operation result in?

• Scalar function

• Vector function

• Undefined

 $\nabla\cdot\left(\nabla f\right)$  
What will this operation result in?

• Scalar function

• Vector function

• Undefined

 $\nabla\times\left(\nabla\times\overrightarrow{F}\right)$  
What will this operation result in?

• Scalar function

• Vector function

• Undefined

Find curl  $\overrightarrow{F}$  :   $\overrightarrow{F}\left(x,y,z\right)=<x^2,\ y-z,\ xe^y>$  

•  $<xe^y+1,\ -e^y,\ 0>$  

•  $<xe^y+1,\ e^y,\ 0>$  

•  $<xe^y-1,-e^y,\ 0>$  

•  $<xe^y-1,\ e^y,\ 0>$  

Find div  $\overrightarrow{F}$  :   $\overrightarrow{F}\left(x,y,z\right)=<x^2,\ y-z,\ xe^y>$  

• 2x + 1

• 2x - 1

•  $2x+xe^y$  

•  $2x+1+xe^y$  

The divergence at point P is...

• positive

• negative

• zero

The divergence at point P is...

• positive

• negative

• zero

The vector field $\overrightarrow{F}\left(x,y,z\right)=<y^2,\ x^2e^z,\ \cos\left(xy\right)>$ is...

• conservative and incompressible.

• not conservative and incompressible

• conservative and not incompressible

• not conservative and not incompressible

The vector field $\overrightarrow{F}\left(x,y,z\right)=<-2xy,\ z^2\cos\left(yz^2\right)-x^2,\ 2yz\cos\left(yz^2\right)>$ is...

• conservative and incompressible.

• not conservative and incompressible

• conservative and not incompressible

• not conservative and not incompressible