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Math Help - Finding the plane of intersection of two spheres in Euclidian (3D) space.

  1. #1
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    Finding the plane of intersection of two spheres in Euclidian (3D) space.

    so if two spheres intersect (one with centre (1,1,2) and radius R=4 and the other with centre (1,1,4) with radius r=2) (i just made these values up i hope they work). how can you find the PLANE that is defined by the intersection of both spheres (actually it's a circle but let's call it a plane)

    The normal vector of the plane is obvious, it must be the vecto C1C2 (the vector between centre 1 and centre 2)

    but how do you find the known point on the sphere then?


    HELP very appreciated! thanks!
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    The point (1,1,6) is on both spheres.
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  3. #3
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    Quote Originally Posted by Plato View Post
    The point (1,1,6) is on both spheres.
    no, not necessarily, that's only the case if bothe spheres are of equal radius; in this case they are not.
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  4. #4
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    Maybe I am reading you example incorrectly.
    It seems to me that the spheres are: (x-1)^2+(y-1)^2+(z-2)^2=16
    \&~(x-1)^2+(y-1)^2+(z-4)^2=4.
    Did I read the question incorrectly? If not that point works.
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  5. #5
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    Quote Originally Posted by Yehia View Post
    so if two spheres intersect (one with centre (1,1,2) and radius R=4 and the other with centre (1,1,4) with radius r=2) (i just made these values up i hope they work). how can you find the PLANE that is defined by the intersection of both spheres (actually it's a circle but let's call it a plane)

    The normal vector of the plane is obvious, it must be the vecto C1C2 (the vector between centre 1 and centre 2)

    but how do you find the known point on the sphere then?


    HELP very appreciated! thanks!
    The small sphere (r = 2) lies completely inside of the large sphere (r = 4) touching the large sphere at T(1, 1, 6)

    The first sphere has the equation:

    (x-1)^2+(y-1)^2+(z-2)^2=16

    The 2nd sphere has the equation:

    (x-1)^2+(y-1)^2+(z-4)^2=4

    Subtract both equations. You'll get: z - 6 = 0
    which is the equation of the plane which contains the common points of both spheres. With your example the equation describes the tangent plane of both spheres.
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