Another problem on triangles (area, ratios) with vectors now.

**gundanium** · May 16th 2011, 04:46 AM

Let A, B, C be three points on a plane and O be the origin point on this plane. Put
$\vec{a} = \vec{OA}$
$\vec{ b} = \vec{OB}$
and
$\vec{c} = \vec{OC }$
P is a point inside the triangle ABC. Suppose that the rato of the areas of $\Delta PAB, \Delta PBC, \Delta PCA$ is 2:3 :5 respectively

(1) The straight line BP intersects the side AC at point Q
Find AQ:QC

How do I even start with this? Can i assume the triangle to be a right triangle so that things might be easier?

**alexmahone** · May 16th 2011, 05:10 AM

Originally Posted by gundanium

Let A, B, C be three points on a plane and O be the origin point on this plane. Put
$\vec{a} = \vec{OA}$
$\vec{ b} = \vec{OB}$
and
$\vec{c} = \vec{OC }$
P is a point inside the triangle ABC. Suppose that the rato of the areas of $\Delta PAB, \Delta PBC, \Delta PCA$ is 2:3 :5 respectively

(1) The straight line BP intersects the side AC at point Q

How do I even start with this? Can i assume the triangle to be a right triangle so that things might be easier?

What exactly is the question?

**gundanium** · May 16th 2011, 05:12 AM

Originally Posted by alexmahone

What exactly is the question?

Sorry. Find AQ:QC

**Zellator** · May 26th 2011, 05:52 AM

Bump! I'm confused with this question also!
There's a way to do $\Delta QAB, \Delta QBC$
And relate both, can someone enter in details, please?

How do we relate $\Delta QAB, \Delta QBC$ between themselves?

**mr fantastic** · May 26th 2011, 09:14 PM

Originally Posted by Zellator

Bump! I'm confused with this question also!
There's a way to do $\Delta QAB, \Delta QBC$
And relate both, can someone enter in details, please?

How do we relate $\Delta QAB, \Delta QBC$ between themselves?

Popular question. Is it part of an assignment? Thread closed for the time being.

Edit: Re-opened.

**Zellator** · May 29th 2011, 03:10 PM

Thanks for the unlocking mr fantastic.

As someone may erroneously think, this is not for an assignment.
This is an exam question that was made in 2009.
As confirmed by mr fantastic.

The question is still open.
Can someone help us?
Vectors involving geometry and ratios, this is a little confusing.

Thanks!

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