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Math Help - line equation in vectors

  1. #16
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    Re: line equation in vectors

    r = a + λc is equation of line through a in dir of c. r is vector from origin to a point on line and λ is arbitrary parameter. A simple sketch makes this clear.
    Let i, j, k be the usual 3 dimensional basis vectors and assume the given line is in i, j plane. Then kXc is normal to the line and in the plane i, j and the equation of the line through point B (location b) normal to the given line is:

    r = b + λ(kXc)

    EDIT: whoops. line is in general 3d dir. Take a minute to revise. Sorry

    (bXc)Xc is perpendicular to c and in plane of b, c. (difficult to see, actually had to ck with a couple of pencils)

    r = b + λ[(bXc)Xc]
    Last edited by Hartlw; February 6th 2013 at 08:12 AM.
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  2. #17
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    Re: line equation in vectors

    3d version of previous post by Hartlw is wrong.

    Correct Solution:

    Determine r0 = a + λ0c where line from B intersects given line perpendicularly:
    (r0 - b)∙c = 0 → (a + λ0c b).c = 0, determines λ0

    r = b + λ(r0 b)

    Sorry about that. In a way Im glad, because previous solution (wrong) was almost impossible to visualize.
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