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Math Help - Finding vectors of give magnitude that are perpendicular...

  1. #1
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    Finding vectors of give magnitude that are perpendicular...

    Hi guys,

    Just beginning vectors but I am still not grasping the concept that well, I have looked around a bit and tried a few ideas out...

    The question is
    Let v = (4, 2). Find all vectors of magnitude 4 that are perpendicular to v.

    Not entirely sure how to approach this... pretty awful with vectors, I calculated the magnitude of v (root 20), however I really wasn't sure what to do with that afterwards.. any help would be much appreciated.

    Cheers in advance,
    Sim
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  2. #2
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    Re: Finding vectors of give magnitude that are perpendicular...

    Quote Originally Posted by simwun View Post
    Hi guys,

    Just beginning vectors but I am still not grasping the concept that well, I have looked around a bit and tried a few ideas out...

    The question is
    Let v = (4, 2). Find all vectors of magnitude 4 that are perpendicular to v.

    Not entirely sure how to approach this... pretty awful with vectors, I calculated the magnitude of v (root 20), however I really wasn't sure what to do with that afterwards.. any help would be much appreciated.

    Cheers in advance,
    Sim
    1. Let \vec p denotes the perpendicular vector of \vec v

    2. Since \vec v \perp \vec p ~\implies~\vec v \cdot \vec p = 0

    You'll get \overrightarrow{p_1} = \langle -2, 4 \rangle or \overrightarrow{p_2} = \langle 2, -4 \rangle

    3. These vectors have still the magnitude \sqrt{20} = 2 \sqrt{5}

    You are looking for a factor f such that

    f \cdot 2 \sqrt{5} = 4

    Determine f.
    Thanks from simwun
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  3. #3
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    Re: Finding vectors of give magnitude that are perpendicular...

    Ah i see, cheers mate
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