Results 1 to 2 of 2

Thread: triangles represented using vectors

  1. #1
    Newbie
    Joined
    Apr 2008
    Posts
    4

    triangles represented using vectors

    Consider a triangle ABC formed by the vectors a=(2,10,25) and b=(5,4,-2) attached at the point A. I've calculated the area of the triangle as $\displaystyle 40.5\sqrt{5} $ and now need to find the vector h=AM, the height of the triangle [so AM is perpendicular to BC and M lies on the line BC]. I've tried using so many different formulae to try and find h or the third side of the triangle and nothing I get seems sensible. Can someone please give me some hints or suggestions on where to start so I can work through this problem? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2010
    Posts
    1,036
    Thanks
    272
    The line going through $\displaystyle A$ and $\displaystyle B$ is just $\displaystyle A+\gamma(B-A)$, where $\displaystyle \gamma$ is a real number. So $\displaystyle \gamma=0$ gives point $\displaystyle A$ and $\displaystyle \gamma=1$ gives point $\displaystyle B$.

    The altitude $\displaystyle AM$ of the triangle has to be perpendicular to that line, so

    $\displaystyle M\cdot(B-A)=(A+\gamma(B-A))\cdot(B-A)=0$

    which you should be able to solve for $\displaystyle \gamma$, and then find $\displaystyle M$.

    Post again in this thread if you're still having trouble.

    - Hollywood
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Can this series be represented by a function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Oct 11th 2011, 07:58 AM
  2. Replies: 5
    Last Post: May 29th 2011, 03:10 PM
  3. Proof about medians of triangles using vectors
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: Oct 29th 2009, 09:07 PM
  4. can this be represented clearer?
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Apr 1st 2008, 07:37 PM
  5. Vectors and Oblique Triangles
    Posted in the Math Topics Forum
    Replies: 10
    Last Post: Sep 14th 2006, 06:34 PM

Search Tags


/mathhelpforum @mathhelpforum