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P3 vectors . watch

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    P3 vectors .


    Referred to the origin O , the points A and B have position vectors (4i-11j+4k) and (7i+j+7k) respecitvely .

    a) Find a vector equation for the line passing through A and B in terms of a parameter t.
    b) Find the postition vector of the point P on AB such that OP is perpendicular to AB.

    I've found the vector equation of line AB ( 4i-11j+4k + t(3i + 12j + 3k) ... i've no idea how to do part b and similiar other vector questions .... help
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    First, rewrite the equation of line AB:
    r = (4, -11, 4) + t(3, 12, 3) = (4, -11, 4) + t(1, 4, 1) = (4+t, 4t-11, 4+t)

    AB = OB - OA = (7, 1, 7) - (4, -11, 4) = (3, 12, 3)
    OP = (4+t, 4t-11, 4+t), since P lies on the line AB.

    AB . OP = 0, since they're perpendicular.
    (3, 12, 3) . (4+t, 4t-11, 4+t) = 0
    12 + 3t + 48t - 132 + 12 + 3t = 0
    => t = 2

    So:
    OP = (4+2, 8-11, 4+2) = (6, -3, 6)
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    Thanks a lot ... hopefully i'll be able to solve the other questions now :-)
 
 
 
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Updated: May 9, 2005

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