# When gradient is parallel to position vector

1. Apr 15, 2007

### oahsen

1. The problem statement, all variables and given/known data

suppose that grad of f(x,y,z) is always parallel to the position vector xi+yj+zk. show that f(0,0,a)=f(0,0,-a) for any a.

3. The attempt at a solution
grad of f= fx(x,y,z)i+fy(x,y,z)j+fz(x,y,z)k ; then gradf (dot) pos.vector = |gradf|*|pos.vector| (since cos(teta)=1 ) ===> however ı could not do anything with this equation and ı have not any other idea...

2. Apr 15, 2007

### Mathgician

dot product, or cosine of theta

positive if theta is 0, negative if theta is 180 or pi

that tells your max and min slope

3. Apr 15, 2007

### oahsen

what should ı do with the max and min slope value?

4. Apr 15, 2007

### Mathgician

what is the vector from f(0,0,a) to f(0,0,-a)?

find the unit vector of this vector,

and then do the dot product of the unit vector and the gradient vector.

5. Apr 15, 2007

### oahsen

since we do not know f how can we find the vector from f(0,0,a) to f(0,0,-a)?
please be more clear. I do not know perfectly this subject.

6. Apr 15, 2007

### Mathgician

lets call f(0,0,a) point P, and f(0,0,-a) point S

What is vector PS?

7. Apr 15, 2007

### oahsen

is it -2ak (ı am not sure)

8. Apr 15, 2007

### Mathgician

find the unit vector of that and do the dot product of that and the gradiant and see if you get the answer you are looking for