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Line and unit sphere

  1. Sep 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Does the line through the points (−1, −1, −2) and (1, 2, 1) intersect the unit sphere? If so, find the point(s) of intersection.

    2. Relevant equations

    3. The attempt at a solution
    do i also use r = r0 + vt but instead , use equation of sphere this time?

    so it would be:


    then using (-1,-1,-2) as the point

    x = -1 + 2t y = -1 + 3t z=-2 + 3t

    plugging these into x2 + y2 + z2 = 1

    then solve for t

    but then the math gets way too long and just doesn't seem to be the correct approach.
    Last edited by a moderator: Sep 18, 2015
  2. jcsd
  3. Sep 18, 2015 #2


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    You could try finding how close the line gets to the origin. If it's less than 1, it must intersect the unit sphere.
  4. Sep 18, 2015 #3
    do I need to use scalar projection for this?
  5. Sep 18, 2015 #4
    What's wrong with your approach? I used it and got the answer quickly.
  6. Sep 18, 2015 #5

    Ray Vickson

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    The math does not get way too long; it is a bit messy, but sometimes that is how things are.
  7. Sep 18, 2015 #6
    whoops, there seems to be an error from the copy paste, it should be x2 + y2 + z2 = 1 and not x2 + y2 + z2 = 1. I will fix it right now.

    hmmm, I cannot seem to edit my OP.
  8. Sep 18, 2015 #7


    Staff: Mentor

    You can edit your post provided you do so within a short period of time. I have fixed your post for you.
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