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Math Help - Angle in a triangle with three coordinates in space

  1. #1
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    Angle in a triangle with three coordinates in space

    P, Q and R are three points in space with coordinates (2, -1, 4) , (3, 1, 2) and (-1, 2, 5) respectively. Find angle Q in the triangle PQR.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Use the dot product!
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  3. #3
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    Im not sure how!

    There are three coordinates here, but the dot product can only be used with two because the dot product is not associative?

    I tried using the dot product with the vector equations of point P and R (assuming Q is in the middle?) ... I don't seem to get the right equation though. Not sure what I'm doing wrong !
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  4. #4
    MHF Contributor Bruno J.'s Avatar
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    Draw a picture, it helps.

    Let v be the vector QP and u the vector QR. Surely you know how to find these vectors from the points. Then u\cdot v = |u| |v| \cos \theta where \theta is the angle you are looking for.

    Try it and post what you're doing, I'll tell you if it's right.
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