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Thread: 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)
    $\displaystyle \vec{PQ} = \vec{PO}+\vec{OQ}$
    $\displaystyle =-\vec{OP}+\vec{OQ}$

    $\displaystyle = ...$ ?

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

    $\displaystyle = ...$ ?
    (c)
    $\displaystyle PQ:QZ = 3:2$

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

    Grandad
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