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Quickie: vector normal to surface

  1. Oct 16, 2015 #1
    1. The problem statement, all variables and given/known data
    Find vector normal to z = x^2 + y^2 - 3 at point r = (2, -1, 2)

    2. Relevant equations


    3. The attempt at a solution
    normal.png

    here is the markscheme. I understand how to find the gradient, but i dont understand how they calculated the magnitude.

    thanks
     
  2. jcsd
  3. Oct 16, 2015 #2

    Geofleur

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    ## z = x^2 +y^2 - 3 ## is satisfied by points that form a three dimensional surface, and it's helpful to view that surface as the level surface of some function. How about viewing it as the level surface ## f(x,y,z) = 0 ## for ## f(x,y,z) = z - x^2 - y^2 + 3 ##? Does that clarify things?
     
  4. Oct 16, 2015 #3
    nope. Take the magnitude of the llevel surface?
     
  5. Oct 16, 2015 #4

    SteamKing

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    What's the magnitude of the vector -4i + 2j + k ? This is the gradient vector at (2, -1, 2)
     
  6. Oct 16, 2015 #5
    how does that help? i need to know how to compute the magnitude.
     
  7. Oct 16, 2015 #6

    SteamKing

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    Good Lord, you're working gradient problems, but you've skipped basic vector arithmetic.

    If V = ai + bj + ck, then |V| = (a2 + b2 + c2) 1/2

    Also |V| = (VV)1/2, where ⋅ signifies the dot product of two vectors.
     
  8. Oct 16, 2015 #7
    My fault all along. I was trying to calculate the magnitude of the surface instead of the magnitude of the gradient of the surface.

    Yes i know how to calculate the magnitude of a vector thank you very much.

    answered.
     
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