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How can the length of a normal vector matter?

  1. Oct 26, 2013 #1
    1. The problem statement, all variables and given/known data

    qIHY9.png

    2. Relevant equations



    3. The attempt at a solution

    Solution:

    zMjwn.png

    Graph:

    kYSoJ.png

    For part a, I understand mathematically why the value of c matters. What I don't understand is how it can possibly matter intuitively.

    I get that ##\overrightarrow { \nabla } F(x_{ 0 },y_{ 0 },z_{ 0 })=(0,c,0)## and therefore, c can't be any value. My question is: how can a tangent plane possibly depend on the length of the normal vector? If the vector is normal, then the length shouldn't matter because the vector will always be normal for all values for c except 0.
     
  2. jcsd
  3. Oct 26, 2013 #2

    vela

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    You need two pieces of information to specify the plane: the normal and a point on the plane. ##c## goes into figuring out what point the plane passes through.
     
  4. Oct 26, 2013 #3
    What are the effects on a tangent plane when you scale up and down ∇F but keep ∇F in the same direction?
     
  5. Oct 26, 2013 #4

    vela

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    ##\nabla F## is determined by F, so you don't have the freedom to arbitrarily rescale it. If you mean what happens if you say, for example, ##\nabla F = (0, c/2, 0)## instead of ##\nabla F = (0, c, 0)##, why don't you try it and see what happens?
     
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