- Thread starter
- #1

#### skatenerd

##### Active member

- Oct 3, 2012

- 114

It says to find the potential function \(f\) for the vector field \(\vec{F}\). The problem states

$$\vec{F}=(y+z)\hat{i}+(x+z)\hat{j}+(x+y)\hat{k}$$

So I figured that just the simple integral of each section respective to its component direction would give the potential function

$$f=x(y+z)+y(x+z)+z(x+y)+C$$

However, the answer in the back of the book says other wise. It claims that

$$f=x(y+z)+zy+C$$

Now I can kind of recognize that distributing out my original answer would give something similar to this, but wouldn't it really be

$$f=2x(y+z)+2zy+C$$

Which is ultimately

$$f=2xy+2xz+2zy+C$$

Does anyone have any idea how they got to this answer? I'm a little stuck here.