A question on vector geometry

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- Mar 23rd 2010, 01:19 PMjosephkVector geometry
A question on vector geometry

- Mar 24th 2010, 05:44 AMGrandad
Hello josephkFor 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)$\displaystyle \vec{PQ} = \vec{PO}+\vec{OQ}$(ii)$\displaystyle =-\vec{OP}+\vec{OQ}$

$\displaystyle = ...$ ?

$\displaystyle \vec TU = \vec{OP}$(b)$\displaystyle = ...$ ?

$\displaystyle \vec{QM} = \tfrac12\vec{QR}$(c)$\displaystyle = \tfrac12...$ ?$\displaystyle \vec{TM} = \vec{TQ} + \vec{QM}$

$\displaystyle = 2 ... + \tfrac12 ...$ ?

$\displaystyle = ...$ ?

$\displaystyle PQ:QZ = 3:2$Can you fill in the gaps?

$\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.

Grandad