Results 1 to 2 of 2

Math Help - Intersection of two sphere

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    65

    Intersection of two sphere

    Fid the constant c such that at any point of intersection of the two shpere

    (x - c)^2 + y^2 + z^2 = 3 and x^2 + (y - 1)^2 + z^2 = 1

    the corresponding tangent plane will be perpendicular to each other.



    Info for you: the the gradient of f is normal to the tangent plane of a level surface f(x) = c.

    So if the two gradient vectors are perpendicular, then the planes should be too. I found the two gradient vectors and dot product(ed) them together and set them to 0. But I don't know what the intersection is for (I'm getting an equation of a line for the intersection which doesn't make sense). Any help?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,812
    Thanks
    117
    Quote Originally Posted by hashshashin715 View Post
    Fid the constant c such that at any point of intersection of the two shpere

    (x - c)^2 + y^2 + z^2 = 3 and x^2 + (y - 1)^2 + z^2 = 1

    the corresponding tangent plane will be perpendicular to each other.

    ...
    1. The sphere s_1: (x - c)^2 + y^2 + z^2 = 3 has it's center at C_1(c,0,0) and the constant radius r_1=3.

    The sphere s_2: x^2 + (y-1)^2 + z^2 = 1 has it's center at C_2(0,1,0) and the constant radius r_2=1.

    2. The two centers are located in the x-y-plane. I've made a sketch of the situation. (see attachment)

    3. To get at least points of intersections the two centers must have a distance between 4 and 2. Use Pythagorean theorem to determine the value of c.
    Ive got \sqrt{3}\leq |x| \leq \sqrt{15}.

    4. If |c|=\sqrt{3} the smaller sphere touches the larger sphere from the interior; if |c|=\sqrt{15} the smaller sphere touches the larger sphere from the exterior.

    5. If \sqrt{3}< |x| < \sqrt{15} then the points of intersection form a circle.
    Attached Thumbnails Attached Thumbnails Intersection of two sphere-tangentialkugeln.png  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Line, sphere intersection.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 30th 2011, 07:22 PM
  2. Intersection of Plane and Sphere
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 19th 2010, 11:57 AM
  3. Intersection of a sphere with xz plane
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 24th 2010, 03:20 PM
  4. Sphere-line intersection
    Posted in the Calculus Forum
    Replies: 5
    Last Post: June 1st 2010, 12:11 PM
  5. Points of Intersection with sphere
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 6th 2009, 09:32 AM

Search Tags


/mathhelpforum @mathhelpforum