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Math Help - Expressing Vectors

  1. #1
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    Expressing Vectors

    ABCDE is a pentagon such that AB = DC and AC=2ED. Write each vector in terms of AB and AC.

    AE = ?

    The answer they have is -AC -1/2AC

    I can't see to figure out why this is correct. Can someone please explain it to me? Thanks!
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  2. #2
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    Hello john-1
    Quote Originally Posted by john-1 View Post
    ABCDE is a pentagon such that AB = DC and AC=2ED. Write each vector in terms of AB and AC.

    AE = ?

    The answer they have is -AC -1/2AC

    I can't see to figure out why this is correct. Can someone please explain it to me? Thanks!
    That answer is not correct. It should be:
    \vec{AE} = \vec{AC}+\vec{CD}+\vec{DE}
    =\vec{AC}-\vec{AB}-\tfrac12\vec{AC}

    =\tfrac12\vec{AC} -\vec{AB}
    Grandad
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  3. #3
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    Hi Grandad, would you mind retyping your answer? I can't see it because of the LaTeX Error ^
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  4. #4
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by john-1 View Post
    Hi Grandad, would you mind retyping your answer? I can't see it because of the LaTeX Error ^
    Since the forum is being updated, LaTeX is not working yet, but you can still see what Grandad typed by quoting him. He typed:


    [tex]\vec{AE} = \vec{AC}+\vec{CD}+\vec{DE}[/tex]
    [tex]=\vec{AC}-\vec{AB}-\tfrac12\vec{AC}[/tex]

    [tex]=\tfrac12\vec{AC} -\vec{AB}[/tex]


    I could find some way to make an image (or you could), but maybe you can see what it should look like already.
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  5. #5
    MHF Contributor undefined's Avatar
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    Using this site, I got this: (click on image for full size)

    Expressing Vectors-vectors_img.png

    (Rendered without a problem, was kind of hard to download though.)

    Edit: This site seems better for converting LaTeX to image. The way to get a newline is double backslash, \\.
    Last edited by undefined; June 17th 2010 at 03:17 PM.
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  6. #6
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    Hello, john-1

    ABCDE is a pentagon such that \overrightarrow{AB} = \overrightarrow{DC} and \overrightarrow{AC} = 2\!\cdot\!\overrightarrow{ED}.

    Write \overrightarrow{AE} in terms of \overrightarrow{AB}\text{ and }\overrightarrow{AC}.

    The answer they have is: .  -\overrightarrow{AC} -\tfrac{1}{2}\overrightarrow{AC} . This can't be right!

    We have: . \overrightarrow{AE} \;=\;\overrightarrow{AC} + \overrightarrow{CD} + \overrightarrow{DE}

    . . . . . . . . . . . =\;\overrightarrow{AC} - \overrigjhtarrow{DC} - \overrightarrow{ED}

    . . . . . . . . . . . =\;\overrightarrow{AC} - \overrightarrow{AB} - \frac{1}{2}\overrightarrow{AC}

    . . . . . . . . . . . =\;\frac{1}{2}\overrightarrow{AC} - \overrightarrow{AB}
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