Thread: Divergent and rotational

Calculate the div and rot:

Correct?

The divergence is correct

Not sure what you have in mind for rotF

but it is 5z^2 i +3xz^2 j +4 y^4x k

The middle row of the determinant are the operators d/dx d/dy and d/dz
and the last row are the x , y , and z components of F not the parial derivatives

In the middle row is the partial derivatives (div) ?

In the last line components i, j and k of F ?

I solved this way not correct ?

No the middle row is just the operators d/dx etc

Write F =f i + g j + h k

then the last row is f - g - h

Then rotF = (dh/dy-dg/dz)i - (dh/dx-df/dz) j + (dg/dx-df/dy)k

Thank you very much. Look this is correct

Yes except the last term in your calculation of divF should be

-x/(x^2+z^2)

Thanks

How do I calculate :

Compute FxG then compute the divergence of the result

you can also use del*(FxG) = G*(del x F)-F*(del x G)

The symbol means divergent ?

If I have: and have F how can I calculate ?

How can I verify that the vector projection have the property:
1)

is an operator and means d/dx i +d/dy j +d/dz k where d/dx d/dy d/dz ar the partial derivative operators

f is the gradient where f is a scalar valued function

X F is the curl or rotation where F is a vector field

*F is the divergence where F is a vector field * means dot product

From the previous identity * ( x F) = 0

r= xi +yj +zk

||r|| = (x^2 +y^2 +z^2)^(1/2)

Compute ||r|| and the result follows directly

Thanks, you're helping me a lot

check my learning:

1)



My solution:




2)


My solution:




3) Check that:

My solution:



is correct

Looks good you have learned well.

Note

is always 0 regardless of what F is. so you don't have to calculate but it was a good exercise to verify this.

thanks. good Note