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

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

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

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

3. Originally Posted by alexmahone
What exactly is the question?
Sorry. Find AQ:QC

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

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

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

How do we relate $\displaystyle \Delta QAB, \Delta QBC$ between themselves?
Popular question. Is it part of an assignment? Thread closed for the time being.

Edit: Re-opened.

6. 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!