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Math Help - angle between displacement vectors

  1. #1
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    Thumbs up angle between displacement vectors

    Hi,

    what is the angle between these vectors?

    u=(1, -1, sqrt 6) and v = (-1, 1, sqrt 6)

    I used cos theta = a.b/ |a| |b| to get 87.9 degrees but on the multi choice question this isnt one of the answers and i cant see where ive gone wrong.

    Cheers!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ohdearthisisheadrot View Post
    Hi,

    what is the angle between these vectors?

    u=(1, -1, sqrt 6) and v = (-1, 1, sqrt 6)

    I used cos theta = a.b/ |a| |b| to get 87.9 degrees but on the multi choice question this isnt one of the answers and i cant see where ive gone wrong.

    Cheers!
    Hi

    \cos \theta = \frac{\overrightarrow{u}.\overrightarrow{v}}{||\ov  errightarrow{u}||.||\overrightarrow{v||}}=\frac{1\  cdot(-1) + (-1)\cdot 1 + \sqrt{6}\cdot \sqrt{6}}{\sqrt{1^2+(-1)^2+\sqrt{6}^2}\cdot \sqrt{(-1)^2+1^2+\sqrt{6}^2}}

    \cos \theta = \frac{4}{\sqrt{8}\:\sqrt{8}}= \frac{4}{8}=\frac12
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