# Please tell me the definition of this problem!

1. Nov 9, 2009

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

Find the unique vector which is perpendicular on x2+y2=100 at (x0,y0)=(6,8).

2. Relevant equations

$$\nabla$$F$$/$$ $$\left|$$ $$\nabla$$F $$\left|$$

3. The attempt at a solution

I think the solution is $$\nabla$$F$$/$$ $$\left|$$ $$\nabla$$F $$\left|$$ but I don't know how to calculate $$\nabla$$F for x2+y2=100
I know $$\nabla$$F=($$\partial$$F$$/$$$$\partial$$x,$$\partial$$F$$/$$$$\partial$$y,$$\partial$$F$$/$$$$\partial$$z)
Please tell me how I can find the answer. What is F here?

Last edited: Nov 9, 2009
2. Nov 9, 2009

### Dick

F(x,y)=x^2+y^2-100. The level surface is F(x,y)=0. Now do the gradient. Or F(x,y)=x^2+y^2 and the level surface is F(x,y)=100, your choice.

3. Nov 10, 2009

So in this case the solution is $$\nabla$$F$$/$$$$\left|$$$$\nabla$$F$$\left|$$ = (0.6,0.8) Is it correct?
($$\nabla$$F=(2x,2y)).

4. Nov 10, 2009

### Dick

If you mean to find the unit normal to the circle, sure, that's right.

5. Nov 10, 2009