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Thread: Pyramid problem

  1. #1
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    Pyramid problem

    Hi, I have this problem:
    given pyramid SABC that the base is ABC, and the apex is S.
    u,v,w, are vectors with the same size.
    Consider M is a dot in the base so $\displaystyle {\overrightarrow{SM}=\frac{\bf{u}}{3}+\frac{\bf{v} }{3}+\frac{\bf{w}}{3}}$,
    and also, all the angles between the vectors u,v,w are equals.
    I need to prove that $\displaystyle {\overrightarrow{SM} } $ is perpendicular to the plane of the base ABC.
    Pyramid problem-pyr.jpg
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  2. #2
    Junior Member Walagaster's Avatar
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    Re: Pyramid problem

    Quote Originally Posted by xbox360 View Post
    Hi, I have this problem:
    given pyramid SABC that the base is ABC, and the apex is S.
    u,v,w, are vectors with the same size.
    Consider M is a dot in the base so $\displaystyle {\overrightarrow{SM}=\frac{\bf{u}}{3}+\frac{\bf{v} }{3}+\frac{\bf{w}}{3}}$,
    and also, all the angles between the vectors u,v,w are equals.
    I need to prove that $\displaystyle {\overrightarrow{SM} } $ is perpendicular to the plane of the base ABC.
    Click image for larger version. 

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    Hint:$ \vec{AB} =v - u$. What do you get when you dot that into $\vec{SM}$? And similarly for the other two sides of the base.
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