Results 1 to 4 of 4

Math Help - Vector problem

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    11

    Vector problem

    Let ABC be a triangle with AB=\vec{a} and AC=\vec{b} and M\in[BC], \frac{BM} {MC}=k.
    AM= ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    We have \overrightarrow{BM}=k\cdot\overrightarrow{MC}

    \overrightarrow{BM}=\overrightarrow{AM}-\overrightarrow{AB}

    \overrightarrow{MC}=\overrightarrow{AC}-\overrightarrow{AM}

    Then, \overrightarrow{AM}-\overrightarrow{AB}=k\left(\overrightarrow{AC}-\overrightarrow{AM}\right)\Rightarrow

    \Rightarrow (1+k)\overrightarrow{AM}=\overrightarrow{AB}+k\ove  rrightarrow{AC}\Rightarrow\overrightarrow{AM}=\fra  c{1}{1+k}\overrightarrow{AB}+\frac{k}{1+k}\overrig  htarrow{AC}\Rightarrow

    \overrightarrow{AM}=\frac{1}{1+k}\overrightarrow{a  }+\frac{k}{1+k}\overrightarrow{b}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,579
    Thanks
    1418
    Quote Originally Posted by sillyme View Post
    Let ABC be a triangle with AB=\vec{a} and AC=\vec{b} and M\in[BC], \frac{BM} {MC}=k.
    AM= ?
    Your notation is slightly confusing. You say that AB= \vec{a} so "AB" means the vector from A to B but then you use BM and MC as lengths of vector since you are dividing them. I don't know whether the "AM" you want is to be a vector or a length.

    I am going to call the vector from B to C, [tex]\vec{c}[/itex], the vector from B to M, \vec{m}, and the vector from A to M, \vec{x} and use the capital letters only for the lengths.

    Since \frac{BM}{MC}= k, BM= kMC and BM+ MC= (k+1)MC.
    Then \vec{m}= (BM/(BM+ MC)\vec{c}= (k/k+1)\vec{c}. But \vec{b}= \vec{a}+ \vec{c} so \vec{c}= \vec{b}- \vec{a} and then \vec{m}= (k/(k+1))(\vec{b}- \vec{a}) so, finally, \vec{x}= \vec{a}+ \vec{m}= \vec{a}+ (k/(k+1))(\vec{b}- \vec{a})) = (1/(k+1)\vec{a}+ (k/(k+1))\vec{b}

    The distance AM is the length of the vector \vec{x} above.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2009
    Posts
    11

    Thanks

    Thank you red_dog!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. vector problem
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: December 10th 2011, 10:17 AM
  2. 3D vector problem
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: May 6th 2011, 08:59 AM
  3. Vector problem
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 3rd 2011, 03:39 PM
  4. vector problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: March 9th 2010, 08:34 AM
  5. vector problem sum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 9th 2009, 08:42 AM

Search Tags


/mathhelpforum @mathhelpforum