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Math Help - Vector triangle problem...

  1. #1
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    Vector triangle problem...

    ABC is a triangle. D is the mid-point of BC, E is the mid-point of AC, F is the mid-point of AB and G is the mid-point of EF. Express the displacement vectors AD and AG in terms of OA, OB, and OC.

    I am totally lost with this one. I have tried several drawings but I guess all of them were wrong. Please help!
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  2. #2
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    Here are two strong hints.
    \overrightarrow {AB}  = \overrightarrow {OB}  - \overrightarrow {OA} \,\& \,\overrightarrow {AD}  = \overrightarrow {AB}  + \frac{1}<br />
{2}\overrightarrow {BC}
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  3. #3
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    Thanks.. But I cannot understand how did that happen. I have been studying vectors for several hours but I don't get it.

    I guess that was from the parallelogram law of vectors? I do understand how can AB be OB - OA but I do not understand how's the AD derived.

    Do you have a link that explains the same concept?
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  4. #4
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    {\color{red}\overrightarrow {AD}}  = \overrightarrow {AB}  + {\color{blue} \frac{1}{2}\overrightarrow {BC}}
    Attached Thumbnails Attached Thumbnails Vector triangle problem...-vect4.gif  
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