Find the divergence and curl of the given vector field

chwala said:

##∇× F = xz i +yzj##

Hennessy said:

p.s this isn't pre calculus Maths as this is Vector Calculus !

Hennessy said:

Looks Good

chwala said:

For divergence i have,

##∇⋅F = (\cos x -x\sin x)i -e^y j +xy k##

Orodruin said:

It does not.

Divergence is a scalar, not a vector.

MatinSAR said:

I think it is a typo but second component should be nagative.

Edit:
Now I think you made a mistake in calculating ##∇× F##.
You can check your final answer using online calculators.

Check this link.

chwala said:

correct- i will just amend my original post...cheers

SammyS said:

When you amend a post after several replies, especially in the case of the OP, it can be very confusing.
So, if you do amend later, please make that very clear in the amended post. - Mention what's amended and why.

SammyS said:

When you amend a post after several replies, especially in the case of the OP, it can be very confusing.
So, if you do amend later, please make that very clear in the amended post. - Mention what's amended and why.

Hennessy said:

Looks Good. One thing to watch out for is make sure your unit vectors have hats on them
like this. p.s this isn't pre calculus Maths as this is Vector Calculus !

$$\hat{i}\: \hat{j}\: \hat{k}$$

Just to avoid confusion. i thought you had i as the complex number and i was like but its derivative would be hyperbolic. Once i figured out i, j and k were your unit vectors all was good, you've differentiated each unit vector component correctly for the divergence and the curl :) Edit: Other peeps have corrected me and it was also my mistake the answer should be scalar and not a vector , apologies for any confuison.