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Finding a plane that contains 2 lines.

  1. Oct 17, 2011 #1
    1. The problem statement, all variables and given/known data

    I have 2 parametric equations of 2 lines. I want to find if there is a plane that contains both, if any, and find the equation.

    2. Relevant equations

    3. The attempt at a solution

    so just thinking about it, I figure that a plane would contain both lines only if they intersect. Is that right?
    if so, my second problem is finding the equation of the said plane. So for both the lines, do I plug in any value of t in the parametric equations to find 2 vectors, take the cross product to find a normal and use that for my equation?
  2. jcsd
  3. Oct 17, 2011 #2


    Staff: Mentor

    No, you could have two parallel lines, and they would determine a plane. The only way two lines would not determine a plane is if they are skew lines - lines that aren't parallel and that don't intersect.

    I'm assuming that you're working in three dimensions.
  4. Oct 17, 2011 #3
    thanks. Totally forgot about the parallel case. So I set my parametric equations equal to each other and found an intersection point. Yes this is in 3 dimensions
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