# Vector geometry

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• Mar 23rd 2010, 01:19 PM
josephk
Vector geometry
A question on vector geometry
• Mar 24th 2010, 05:44 AM
Grandad
Hello josephk
Quote:

Originally Posted by josephk
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