# Del operator

1. Apr 21, 2014

### chemphys1

f(x,y,z) = x2 + y2 + z2

which values of x,y,z does ∇f point in the positive z direction

ok so I know ∇f = i ∂/∂x + j ∂/∂y + k ∂/∂z

which turns out to be

∇f = 2x i + 2y j + 2z k

but how am I finding values so that z points in the positive direction? what does that even mean?
∇f is gradient, could it have specified x direction or y direction, if so what would differ about how to answer the question?

any help/explanation much appreciated

2. Apr 21, 2014

### micromass

I guess they mean that a vector points in the positive $z$-direction if it is of the form $(0,0,k)$ for $k>0$. Does that help?

3. Apr 21, 2014

### chemphys1

I don't recognise this kind of question, how would I go about finding this vector?

4. Apr 21, 2014

### micromass

For which $(x,y,z)$ is the gradient $(2x,2y,2z)$ of the form $(0,0,k)$ for $k>0$.

5. Apr 21, 2014

### chemphys1

is it as simple as follows:
x = 0
y= 0
z = any positive integer?

6. Apr 21, 2014

### micromass

Yes.

7. Apr 21, 2014

### LCKurtz

Almost. You mean any positive number.

8. Apr 21, 2014

### chemphys1

Thank you for the help, it really is appreciated!