Divergence and Curl

[keysar]

What is the curl and divergence here?

F(x,y,z) = (x² + y² - xyz, xz² cos y, z² e^(x²+y²))

 

[Deleted member 4993]

What is the curl and divergence here?
F(x,y,z) = (x² + y² - xyz, xz² cos y, z² e^(x²+y²))

What is the definition of curl and divergence?

Please show us your work, indicating exactly where you are stuck - so that we know where to begin to help you.

 

[galactus]

Curl is found by using the partials.

Given \(\displaystyle F(x,y,z)=f(x,y,z)i+g(x,y,z)j+h(x,y,z)k\)

\(\displaystyle \text{curl \;\ F}=\left(\frac{dh}{dy}-\frac{dg}{dz}\right)i+\left(\frac{df}{dz}-\frac{dh}{dx}\right)j+\left(\frac{dg}{dx}-\frac{df}{dy}\right)k\)