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Silly question

  1. Aug 12, 2009 #1
    Gradient and velocity

    Just curious

    Let's say I have a plane with the equation

    4x + 5y + 6z = 45

    If I find [tex]\nabla[/tex]F(x,y,z) and then find it's magnitude, I get the direction of steepest descent/ascent in the direction of <[tex]\partial[/tex]F(x,y,z)/[tex]\partial[/tex]x,[tex]\partial[/tex]F(x,y,z)/[tex]\partial[/tex]y, [tex]\partial[/tex]F(x,y,z)/[tex]\partial[/tex]z> and the magnitude of the vector in that direction right?

    How would I find the velocity vector of a particle from the top of the plane to the bottom in the direction of the gradient vector? Would I just think of it as an inclined plane? And how is velocity related to finding the gradient?
     
    Last edited: Aug 12, 2009
  2. jcsd
  3. Aug 12, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi seamonkeydoo! Welcome to PF! :smile:
    uhh? It is an inclined plane! :confused:

    Yes, the gradient vector "downhill" is the same as an actual vector "downhill".

    Generally, the gradient vector of a curved surface is the same as the actual "downhill" vector of the tangent plane. :wink:
    It'll be proportional to the gradient.
     
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