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Math Help - Finding a vector from the sides of a triangle

  1. #1
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    Finding a vector from the sides of a triangle

    In a triangle ABC the point M is located on the side BC such that the ratio of
    the lengths of the segments BM and MC is L,
    i.e., lBMl: lMCl= L.
    Find the vector AM given that AB = b and AC = c.
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  2. #2
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    Hello knuckles1234
    Quote Originally Posted by knuckles1234 View Post
    In a triangle ABC the point M is located on the side BC such that the ratio of
    the lengths of the segments BM and MC is L,
    i.e., lBMl: lMCl= L.
    Find the vector AM given that AB = b and AC = c.
    Using the law of addition of vectors
    \vec{AB}+\vec{BC}=\vec{AC}
    \Rightarrow \vec{BC}=\vec{c}- \vec{b}

    \Rightarrow \vec{BM}= \frac{L(\vec{c}- \vec{b})}{L+1}

    \Rightarrow \vec{AM} = \vec{AB}+\vec{BM}=\vec{b} +\frac{L(\vec{c}- \vec{b})}{L+1}
    = \frac{\vec{b} +L\vec c}{L+1}
    Grandad
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