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Homework Help: Angle Between two surfaces and a point

  1. Sep 2, 2008 #1
    Find the angle between the surfaces defined by r^2= 9 and x + y + z^2= 1 at the point (2,-2,1)? --- I know this should be extremely simple but it is blowing my mind for some reason. Any help would be greatly appreciated.
  2. jcsd
  3. Sep 3, 2008 #2


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    The angle between two surfaces at a point pf intersection is the angle between their normal vectors at that point. And if you write the surfaces as f(x,y,z)= constant, the normal vector is in the same direction as [itex]\nabla f[/itex]. You probably want to write the first surface in Cartesian coordinates as x2+ y2+ z2= 9. Find the gradients of those two functions and then use the fact that
    [itex]\vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta)[/itex] where [itex]\theta[/itex] is the angle between the two vectors.

    Although this was posted in Precalculus, I don't believe this can be done without using Calculus.
    Last edited by a moderator: Sep 3, 2008
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