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Math Help - [SOLVED] Two simple problems

  1. #1
    Senior Member Spec's Avatar
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    [SOLVED] Two simple problems

    You're not supposed to use vector/scalar multiplication tricks for these problems.

    1) The point C divides the vector AB in the ratio 1:3. Show that \overline{OC} = \frac{3}{4}\overline{OA} + \frac{1}{4}\overline{OB}

    2) u,\ e_1,\ e_2 are in the same plane.

    |u| = 2, |e_1| = 2, |e_2| = 1
    The angle between e_1 and e_2 is \frac{2\pi}{3}, and \frac{\pi}{6} between u and e_1.

    Write u as a linear combination of e_1 and e_2.

    Note that this will give two possible answers.
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  2. #2
    Senior Member Spec's Avatar
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    1)

    \overline{AB} = \overline{OB} - \overline{OA}

    \overline{OC} = \overline{OA} + \frac{1}{4}\overline{AB}

    \overline{OC} = \overline{OA} + \frac{1}{4}(\overline{OB} - \overline{OA}) = \frac{3}{4}\overline{OA} + \frac{1}{4}\overline{OB}
    Last edited by Spec; August 25th 2008 at 07:16 AM.
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