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Homework Help: Normal vector

  1. Aug 3, 2008 #1
    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
     

    Attached Files:

  2. jcsd
  3. Aug 3, 2008 #2

    Dick

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    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.
     
  4. Aug 3, 2008 #3
    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...:smile:
     
  5. Aug 3, 2008 #4

    Defennder

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    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.
     
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