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Math Help - Vector-finding distance, difficult/confusing

  1. #1
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    Vector-finding distance, difficult/confusing

    Find the distance of the point (1,+ and-6,-1) from the line with vector equation r=i+7j+-1k+t(3i+12j-4k)
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  2. #2
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    Quote Originally Posted by kingkaisai2
    Find the distance of the point (1,+ and-6,-1) from the line with vector equation r=i+7j+-1k+t(3i+12j-4k)
    1) (1,+ and-6,-1) is not a point but if anything it is two points (1, 6,-1) and
    (1,-6,-1).

    2) By the distance from the point p to the line r(t) I take it that you mean
    the minimum distance.

    One way (not necessarily the simplest) to do this is to write:

    s(t)^2=|p-r(t)|^2,

    then differentiate this with respect to t and set the derivative to zero and
    and solve the resulting equation for t, which will give the t corresponding to
    the closest point on the line to the given point, which can then be used to
    find the actual minimum distance.

    RonL
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