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Find a normal vector to a graph

  1. Oct 25, 2015 #1


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    How do you find a normal vector of a function at a point, such as f(x,y)= ax^y+yx^y^x+b at (X_o,Y_o)

    where a and b are just arbitrary constants, and the function is an arbitrary function. So I guess, what is the general steps you take to find the normal? I thought it had to do with the gradient, but I'm still confused.
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  3. Oct 25, 2015 #2


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    It's a normal to the surface defined by the function, not a normal to the function.

    Off the top of my head, one way would be to find the tangent vectors to the surface in the x direction and in the y direction, and take the cross-product..
  4. Oct 26, 2015 #3


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    You can find the tangent plane of the graph at the point ##\left(x_{0},y_{0}\right)##. The coefficients of the tangent plane ## n_{1}x+n_{2}y+n_{3}z+c=0## are the component of the normal vector ## \vec{n}=\left(n_{1},n_{2},n_{3}\right)## of the plane that is a normal vector of ##f(x,y)## at the given point ...
  5. Oct 28, 2015 #4


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    Given a surface described by z= f(x, y),the surface can be thought of as a "level surface for the function [itex]\phi(x, y, z)= f(x, y)- z= 0[/itex] so [itex]\nabla (f(x,y- z)= f_x\vec{i}+ f_y\vec{j}- \vec{k}[/itex] is immediately a vector normal to the surface.
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