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Math Help - Help with Problem

  1. #1
    fiveluck
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    Help with Problem

    Q: Find a line perpendicular and intersecting the lines: (t, 1-t, 2t) and (2t, t, t).

    What I am thinking so far:
    Treat the second line like (2s, s, s)

    Normal Vector: Cross Product of the two: (t-3t^2, 3t^2, 3t^2 - 2t)

    Find 2 equations using cross product then solve for s and t.

    Need help Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by fiveluck
    Q: Find a line perpendicular and intersecting the lines: (t, 1-t, 2t) and (2t, t, t).

    What I am thinking so far:
    Treat the second line like (2s, s, s)

    Normal Vector: Cross Product of the two: (t-3t^2, 3t^2, 3t^2 - 2t)

    Find 2 equations using cross product then solve for s and t.

    Need help Thanks!
    Let the points on the perpendicular at which it intersects the two
    lines be u and v. Then u and v are the points for which the distance
    between points on the two lines is minimised.

    So express the distance between a pair of points, one on one line
    and the other on the second line, in terms of t and s, then find
    the values of t and s which minimise the distance between the
    two points. This will alow you to find the required points, then
    you need only find the line through these two points to answer the
    question.

    RonL
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