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Math Help - The difference between a gradient vector to a surface and the normal vector to that s

  1. #1
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    The difference between a gradient vector to a surface and the normal vector to that s

    ...urface. Plz help I don't understand this difference. Thanks
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  2. #2
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    Re: The difference between a gradient vector to a surface and the normal vector to th

    Hey nicksbyman.

    If you have a definition, you should post it (if its from lectures notes or a book) but a gradient vector can refer to the tangential vector with respect to a particular variable (i.e. one based on the partial derivative of the surface at a particular point).

    It's hard to say with certainty without knowing more information.
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  3. #3
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    Re: The difference between a gradient vector to a surface and the normal vector to th

    I think your problem is where you refer to the "gradient vector" of a surface. There is no such thing. Rather, the gradient vector is the gradient of a function. If we have a function f(x,y,z) then the "gradient of f", also written \nabla f, is the "vector" \frac{\partial f}{\partial x}\vec{i}+ \frac{\partial f}{\partial y}\vec{j}+ \frac{\partial f}{\partial z}\vec{k}. Given such a function, the equation f(x,y,z)= constant, could, theoretically, be "solved" for one of the variables in terms of the other two. Since we can then have z= g(x,y), say, that equation defines a surface. Given the equation f(x,y,z)= C, \nabla f, the gradient vector of the function is a normal vector to the surface at every point.

    (In Britain, the term "gradient" can be used to refer to the derivative of a function, which then is the slope of the tangent line. Chiro may be thinking of that situation. Why in the world can't those Brits speak English!)
    Last edited by HallsofIvy; November 1st 2012 at 07:08 PM.
    Thanks from MarkFL
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