Finding x,y,z for ∇f Pointing in +z Direction

[chemphys1]

f(x,y,z) = x² + y² + z²

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

 

[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?

 

[chemphys1]

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?

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

 

[micromass]

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

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

 

[chemphys1]

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

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

 

[micromass]

Yes.

 

[LCKurtz]

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

Almost. You mean any positive number.

 

[chemphys1]

Thank you for the help, it really is appreciated!