What is the potential of this vector field?
$$20\frac{x}{z}i+14\frac{y}{z}j+\Bigl(1−\frac{10x^2+7y^2}{z^2}\Bigr)k$$
I can't seem to get the right answer. I have to type in the answer for our assignment, but I don't get how to do it. what is the answer, and how do I do it?
Hint for one possibility: if $\vec F$ is a vector field with some conditions the potential of $F$ is given by: $$f(\vec x) = \int_0^1 \vec F(t\vec x)\cdot\vec x\,dt.$$ (in your case you will need "move" this formula)
Alternatively: if your field is $= \nabla f$: $$ \frac{\partial f}{\partial x} = 20\frac{x}{z}, $$ $$ \frac{\partial f}{\partial y} = 14\frac{y}{z}, $$ $$ \frac{\partial f}{\partial z} = \Bigl(1−\frac{10x^2+7y^2}{z^2}\Bigr). $$