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Math Help - Equations of Lines

  1. #1
    Member
    Joined
    Nov 2007
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    Please Close Thread!

    I DON'T KNOW HOW TO RETRIEVE THE TEXTBOOK ANSWER!


    QUESTION:
    Show that the lines:
    r = (4,7,-1) + t(4,8,-4)
    r = (1,5,4) + u(-1,2,3)

    intersect at right angles and find POI.


    ============================

    ATTEMPT:

    v = (4,8,-4) x (-1,2,3)
    v = (32,-8,16)
    v = (4,-1,2)


    Finding POI:

    l_1:
    x = 4 + 4t
    y = 7 + 8t
    z = -1 - 4t

    l_2:
    x = 1 - u
    y = 5 + 2u
    z = 4 + 3u

    (1) 3 = -u - 4t
    (2) 2 = 2u - 8t
    (3) -5 = 3u + 4t

    Find "t", sub (1) into (2):
    t = 1/2

    Find "s", sub "t" into (2):
    u = 3

    Verify (3):
    LS:
    = -5
    RS:
    = 3(3) + 4(1/2)
    = 11

    Therefore, LS does not equal RS, so skew


    ========================


    TEXTBOOK ANSWER:

    (2,3,1)
    Last edited by Macleef; March 17th 2008 at 06:05 PM.
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  2. #2
    Member Henderson's Avatar
    Joined
    Dec 2007
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    2
    Two problems:

    t=\frac{-1}{2}
    The negative sign is important- it'll give you a different value for u, also.

    To show two vectors are perpendicular, use the dot product, not the cross product.
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