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Homework help

  1. Jul 17, 2004 #1
    Got a problem which should be easy but having trouble...

    "Find the equation of the tangent plane to z=f(x,y)=x^2 + y^2 - 1 at point (1,1,1)
    "Find an equation to a plane that is perpendicular to that tangent plane and also passes through the point (1,1,1)

    Thanks!
     
  2. jcsd
  3. Jul 17, 2004 #2

    arildno

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    Welcome to PF!

    Are you familiar with the theorem that the gradient of a surface G(x,y,z)=0 is normal to that surface?
    Use that hint (G(x,y,z)=z-f(x,y)).
     
  4. Jul 17, 2004 #3
    I figured out the first part of the problem the tangent plane to f(x,y) is 2x+2y-z-3=0. The normal vector of that plane is thus <2,2,-1>. I am lost on how to solve the next part, I keep trying different equations but coming up with too many variables.
     
  5. Jul 17, 2004 #4

    arildno

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    There's an infinity of planes which are normal to the tangent plane.
    Pick one of them; the requirement is merely that some tangent vector in the tangent plane should be the normal to the plane you choose.
    (the normal of the tangent plane is to be a tangent vector in the plane you choose)
     
    Last edited: Jul 17, 2004
  6. Jul 17, 2004 #5

    Gokul43201

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    "too many variables" only allows you to set one of them to any convenient value. Like arildno said, there are an infinite number of normal planes passing through a given point; so you get to pick any one you like.
     
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