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

  1. #1
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    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
    \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?
    Last edited by gundanium; May 16th 2011 at 05:12 AM.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by gundanium View Post
    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?
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  3. #3
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    Quote Originally Posted by alexmahone View Post
    What exactly is the question?
    Sorry. Find AQ:QC
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  4. #4
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    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?
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  5. #5
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    mr fantastic's Avatar
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    Quote Originally Posted by Zellator View Post
    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.
    Last edited by mr fantastic; May 26th 2011 at 09:51 PM.
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  6. #6
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    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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