Results 1 to 4 of 4

Math Help - Vector addition triangle medians

  1. #1
    Member sinewave85's Avatar
    Joined
    Oct 2006
    From
    Lost in a series of tubes.
    Posts
    218

    Vector addition triangle medians

    "In a triangle, let u, v, and w be the vectors from each vertex to the midpoint of the opposite side. Use vector methods to show that u + v + w = 0."

    I found an answer to the problem here, but I am still confused. Could someone explain the logic in a little more detail?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,649
    Thanks
    1597
    Awards
    1
    Suppose that \vec{a},~\vec{b},~\&~\vec{c} are the sides of the triangle.
    Then in some order we would have  \vec{u} =\vec{a}+0.5 \vec{b},~\vec{v} =\vec{b}+0.5 \vec{c},~\&~\vec{w} =\vec{c}+0.5 \vec{a} .

    Notice that  \vec{a}+ \vec{b}+ \vec{c}=0.
    Attached Thumbnails Attached Thumbnails Vector addition triangle medians-untitled.gif  
    Last edited by Plato; September 16th 2010 at 03:14 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member sinewave85's Avatar
    Joined
    Oct 2006
    From
    Lost in a series of tubes.
    Posts
    218
    Forgive me, I may have forgotten (or never learned) the rule that is be critical to this problem. Is it a generally understood fact that the vector sum of the sides of a triangle is 0 (i.e. this is not something that I would have to prove in my answer)?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member sinewave85's Avatar
    Joined
    Oct 2006
    From
    Lost in a series of tubes.
    Posts
    218
    Disregard my last post. I get it. Thank you very much!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triangle and Perpendicular medians
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 17th 2011, 03:35 PM
  2. Concurrency of triangle medians.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: September 8th 2010, 01:11 PM
  3. Medians of a triangle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: November 1st 2009, 02:11 AM
  4. Length of Triangle Medians
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 16th 2009, 02:33 PM
  5. Replies: 4
    Last Post: May 14th 2009, 08:34 AM

Search Tags


/mathhelpforum @mathhelpforum