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Math Help - Points of Intersection with sphere

  1. #1
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    Points of Intersection with sphere

    Find the points of intersection of the line r=(0,5,3) +t(1,-3,-2) with the sphere x^2+y^2+z^2=6. Is the segment of the line between the intersection points a diameter of the sphere?

    I'm not sure what I am doing wrong (obviously a lot) since I can't get the right answer with the back of my textbook. Please fix my errors and demonstrate the correct approach. Thanks!

    x/1 = (y-5)/-3 = (z-3)/-2

    x^2 = x=6
    x^2-x-6=0
    x=-3 or x=2
    Last edited by john-1; September 6th 2009 at 09:53 AM.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    replace x,y,and z with parametric forms and solve for t


    t^2 + (5-3t)^2 + (3-2t)^2 = 6


    14t^2 - 42 t + 28 = 0

    (t-2)(t-1) = 0

    t= 1 or 2 you get

    (1,2,1) and (4,-1,-1)
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