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Math Help - c4 vector question

  1. #1
    Junior Member
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    Jun 2008
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    c4 vector question

    The point A with coordinates (0,-5,11) lies on the line l1, which has equation

    r=6i+19j-k+(lamda)
    (i+4-2k)

    The point p lies on l1 and is such that OP is perindicular to l1, where O is the origin.

    Find the position vectore of point P.

    Given that B had coordinates (5,15,1)

    Show that the points A, P and B are collinear and find ratio AP:PB

    Thanks

    Bryn
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  2. #2
    Super Member
    Joined
    Oct 2007
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    London / Cambridge
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    Have you found the values of \lambda that corresponds to each point a , b and p ?

    Once you find them you can consider differences of values of \lambda as distances between points on the line, that should help with finding the ratio.

    Finding the values of \lambda for a should not be a problem

    for p, your given it lies on l_{1} so the position of p is \left(\begin{array}{c}6 + \lambda \\19 + 4 \lambda \\-1 - 2 \lambda\end{array}\right) and you're given that OP it is perpendicular to the the line l_{1} so \left(\begin{array}{c}6 + \lambda \\19 + 4 \lambda \\-1 - 2 \lambda\end{array}\right) \cdot \left(\begin{array}{c}6 \\19 \\-1\end{array}\right) = 0, So now you can solve for \lambda

    Bobak
    Last edited by bobak; June 7th 2008 at 10:23 AM.
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