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Math Help - Vector Problem

  1. #1
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    Vector Problem

    How do I solve this problem using vector analysis?

    Vector Problem-image.jpg
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  2. #2
    MHF Contributor
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    Re: Vector Problem

    Let $\overrightarrow{OB}=b$ and $\overrightarrow{AB}=a$. Express in turn the following vectors through $a$, $b$, $m$ and $n$:
    \[
    \overrightarrow{OA},\quad\overrightarrow{OP}, \quad\overrightarrow{OQ}, \quad\overrightarrow{AC}, \quad\overrightarrow{AQ}.
    \]
    Then from $\triangle OAQ$ we have $\overrightarrow{OA}+ \overrightarrow{AQ}+ \overrightarrow{QO}=0$. Use the fact that
    \[
    \alpha a+\beta b=0\iff \alpha=0\text{ and }\beta=0
    \]
    since $a$ and $b$ are linearly independent.
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