# Vector geometry

• March 23rd 2010, 01:19 PM
josephk
Vector geometry
A question on vector geometry
• March 24th 2010, 05:44 AM
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)
$\vec{PQ} = \vec{PO}+\vec{OQ}$
$=-\vec{OP}+\vec{OQ}$

$= ...$ ?

(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?