# Thread: Conservative Vector Field

1. ## Conservative Vector Field

Determine whether or not the vector field is conservative.
If it is conservative, find a function f such that F = ∇f.

F(x, y, z) = yz i + xz j + xy k

I found the vector field to be conservative but how do I find the function?

The book's answer is xyz + K.

2. ## Re: Conservative Vector Field

Originally Posted by USNAVY
Determine whether or not the vector field is conservative.
If it is conservative, find a function f such that F = ∇f.

F(x, y, z) = yz i + xz j + xy k

I found the vector field to be conservative but how do I find the function?

The book's answer is xyz + K.
I gave a complete out line how these are done. Use it.

In this one $I(x,y,z)=yz,~J(x,y,z)=xz,~\&~K(x,y,z)=xy$

3. ## Re: Conservative Vector Field

Yes, I must integrate to find the function.