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Math Help - Vector geometry

  1. #1
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    Vector geometry

    A question on vector geometry
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  2. #2
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    Hello josephk
    Quote Originally Posted by josephk View Post
    A question on vector geometry
    For easier reference, I've attached the image file in your Word document as a .jpg.

    Here are some suggestions. I'll leave some of the details to you.

    (a) (i)
    \vec{PQ} = \vec{PO}+\vec{OQ}
    =-\vec{OP}+\vec{OQ}

    = ... ?

    (ii)
    \vec TU = \vec{OP}
    = ... ?
    (b)
    \vec{QM} = \tfrac12\vec{QR}
    = \tfrac12... ?
    \vec{TM} = \vec{TQ} + \vec{QM}
    = 2 ... + \tfrac12 ... ?

    = ... ?
    (c)
    PQ:QZ = 3:2

    \Rightarrow \vec{QZ} = \frac23\vec{PQ}
    = ... ? (Use your answer to (a) (i))
    \vec{TZ} = \vec{TQ} + \vec{QZ}
    = ... ? (Express this in terms of \vec p and \vec q.)
    You should now find that \vec{TZ} is a scalar multiple of \vec{TM}. This proves that T,\; M and Z are collinear.
    Can you fill in the gaps?

    Grandad
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