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Math Help - Lines and Planes

  1. #1
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    (solved) Lines and Planes

    Hi, I'm not sure how to solve the following problem.

    Find the parametric equations of a line and a plane that intersects at the point (1,4,-1).

    I know how to find the point of intersection of a line and a plane, but I have no idea how to go backwards.

    Any help would be appreciated.

    Thanks,
    Sam
    Last edited by sam314159265; April 1st 2010 at 08:01 AM.
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  2. #2
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    Thumbs up

    I don't think you have given enough information in the question. the line or the plane could be pointing in any direction as long as they pass through the point you have stated. Does it say if the line is normal to the plane for example?
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  3. #3
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    Quote Originally Posted by sam314159265 View Post
    Hi, I'm not sure how to solve the following problem.

    Find the parametric equations of a line and a plane that intersects at the point (1,4,-1).

    I know how to find the point of intersection of a line and a plane, but I have no idea how to go backwards.

    Any help would be appreciated.

    Thanks,
    Sam
    Do you understand that there are an infinite number of planes and lines through any given point?

    One answer is to take the line to be x= 1, y= 4, z= t and the plane to be z= -1.

    I'm sure you can think up many different answers to this same question!
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  4. #4
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    Yeah, I can't believe I didn't think of that... The question makes a lot more sense now. Thanks for the help
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