# Homework Help: Normal vector

1. Aug 3, 2008

### asi123

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

I took 2 plots.
Can someone explain to me why the first one comes out positive and second negative?

2. Relevant equations

3. The attempt at a solution

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2. Aug 3, 2008

### Dick

If (a,b,c) is normal to a surface, so is (-a,-b,-c). There are two normals to a surface at a given point. For example in the first one you could also have written the plane -x-y-z=0. It's the same plane.

3. Aug 3, 2008

### asi123

Yeah, but why did it switch it on the second one, and the first one stayed positive?
If I learned anything, it is that there is no random in math...

4. Aug 3, 2008

### Defennder

Um, what do you mean by "switch"? I can't make out the coefficient of y in the equation of plane for the second one. You could use the right-hand screw rule along with r_u X r_v to see which direction the normal vector points. It all depends on how you parametrise it. If you had done u=y, v=x for the second one, it would have been the same as the normal vector read off the equation of the plane.