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Math Help - To find a point on a line (in euclidian space) given it intersects two other lines?

  1. #1
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    To find a point on a line (in euclidian space) given it intersects two other lines?

    I've been stumped ever since i heard this one, please help.
    so given that a line is parallel to the x axis (so the direction vector = lambda( 1i + 0j + 0k)

    and given it intersects two other KNOWN lines, how can you go about fiinding the equation of that line (that intersects the two lines).


    technically all you need now is a know point (because we already have the direction vector), but i can't find out how!


    help much appreciated thanks!!
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  2. #2
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    Quote Originally Posted by Yehia View Post
    I've been stumped ever since i heard this one, please help.
    so given that a line is parallel to the x axis (so the direction vector = lambda( 1i + 0j + 0k)
    and given it intersects two other KNOWN lines, how can you go about fiinding the equation of that line (that intersects the two lines).
    technically all you need now is a know point (because we already have the direction vector), but i can't find out how!
    I think that is just far too vague to answer.
    Can you post an actual problem?
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  3. #3
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    Quote Originally Posted by Plato View Post
    I think that is just far too vague to answer.
    Can you post an actual problem?
    Ok sure,

    A line (in 3D euclidian space) that we are interested in finding is parallel to the x-axis.

    Furthermore, it cuts the lines d and l

    d = (2 + )i + (2 + 2)j + (2)k

    and l = (2)i + (3λ)j + (2λ)k

    (where λ and are parameters)

    so how can you find the equation of that line? all i know now is that it has the direction vector (λi + 0j + 0k)...
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  4. #4
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    Quote Originally Posted by Yehia View Post
    A line (in 3D euclidian space) that we are interested in finding is parallel to the x-axis.
    Furthermore, it cuts the lines d and l
    d = (2 + )i + (2 + 2)j + (2)k
    and l = (2)i + (3λ)j + (2λ)k (where λ and are parameters)
    so how can you find the equation of that line? all i know now is that it has the direction vector (λi + 0j + 0k)...
    I may not understand your question.
    But I do not think that such a line can exists.
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