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Math Help - Vector- closest to the point

  1. #1
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    Vector- closest to the point

    The line l has vector equation r=2i+s(i+3j+4k), Determine the position vector of the point on l which is closest to the point with position vector 6i-j+3k

    urgent
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  2. #2
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    Quote Originally Posted by kingkaisai2
    The line l has vector equation r=2i+s(i+3j+4k), Determine the position vector of the point on l which is closest to the point with position vector 6i-j+3k

    urgent
    Write \bold v=\bold{i}+3\bold{j}+4\bold{k}, \bold r(s)=2\bold i+s\bold v and \bold x=6\bold i-\bold j+3\bold k.

    Then solve:

    \bold v\cdot (\bold r(s)-\bold x)=0

    for s, which should work as \bold v is a vector pointing along the line,
    and the vector from \bold x to the closest point on the line is at orthogonal to \bold v.

    RonL
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