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Math Help - Vectors #1

  1. #1
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    Vectors #1

    A spider builds a web in a garden. The position vectors of the ends A andB relative to an origin O of a strand of the web are given by OA = 2i + 3j + k and OB = 3i + 4j + 2k. Another web strand MN has end points M and N with position vectors OM = 4i + 2j - k and ON = 6i + 10j + 9k. The spider decides to continue AB to join MN. Find the position vector of the point of contact.

    I worked out AB to be i + j + k, but I don't know where to go from there. We've just started vectors so most of this is new to me.

    Thanks.
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  2. #2
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    Re: Vectors #1

    Quote Originally Posted by Fratricide View Post
    A spider builds a web in a garden. The position vectors of the ends A andB relative to an origin O of a strand of the web are given by OA = 2i + 3j + k and OB = 3i + 4j + 2k. Another web strand MN has end points M and N with position vectors OM = 4i + 2j - k and ON = 6i + 10j + 9k. The spider decides to continue AB to join MN. Find the position vector of the point of contact.

    I worked out AB to be i + j + k, but I don't know where to go from there. We've just started vectors so most of this is new to me.

    Thanks.
    $\vec{AB}=\vec{OB}-\vec{OA}$

    $\vec{MN}=\vec{ON}-\vec{OM}$

    $L_{AB}(t)=\vec{OB}+t\vec{AB}$

    $L_{MN}(s)=\vec{OM}+s\vec{MN}$

    solve for $L_{AB}(\hat{t})=L_{MN}(\hat{s})$

    then the point of intersection is $L_{AB}(\hat{t})=L_{MN}(\hat{s})$

    The answer here is
    Spoiler:
    (5,6,4)
    Thanks from Fratricide
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