Im having some trouble understanding some concepts with gradient fields. The ultimate goal is to add two gradient fields and then take the divergence.
So I have these 2 fields: one going in the negative y axis direction at a certain (b) velocity and one that looks like y=-x equation. I am trying to make them into an equation I can take the divergence of. All the divergence problems I have looked at already have the equation given in the form of f(x,y,z) or F(x,y,z)=xyzi + xyzj + xyzk. I think I want to find an equation of the 2nd form. I don't understand how to relate the information I was given into that form.
I think the equation for the gradient going in the -y direction would be F(x,y,z) = 0i-.1667yj+0k. I dont understand how to get the second equation. Then do I just add the components to get the full vector field? And then take the divergence of the added fields?