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Math Help - formula for distance from point to line using cross product.

  1. #1
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    formula for distance from point to line using cross product.

    P is a point that is not on the line L that passes through Q and R. Show the distance d from point P to the line is

    d = |a X b| / |a|

    where a = ->QR and b = ->QP

    so must find the distance from point P(1, 1, 1) to the line through
    Q(0, 6, 8)

    and R(-1, 4, 7)


    ....i tried this and computed:

    a=QR = (-1 -2 -1)

    b=QP=(1 -5 -8)

    i took the cross product of (a X b) and got:

    (16-5) - (8 - (-1) + (5- (-2)

    so, (11 - 9 + 7) / |-1 + -2 + -11|

    the final answer is sqrt(97/3)

    not sure what i've done wrong, think its just a computational error, please help.
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by rcmango View Post
    P is a point that is not on the line L that passes through Q and R. Show the distance d from point P to the line is

    d = |a X b| / |a|

    where a = ->QR and b = ->QP

    so must find the distance from point P(1, 1, 1) to the line through
    Q(0, 6, 8)

    and R(-1, 4, 7)


    ....i tried this and computed:

    a=QR = (-1 -2 -1)

    b=QP=(1 -5 -7) << MISTAKE

    [...]
    For the cross product, I find vector (9, -6, 7)


    Also, if you have a vector ax,y,z), that is a=xi+yj+zk, then |a|=\sqrt{x^2+y^2+z^2}, which was not what you applied here :s

    So try again with that
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