Results 1 to 3 of 3

Math Help - vector example explination.

  1. #1
    Member
    Joined
    Apr 2010
    Posts
    135

    vector example explination.

    hello, can some one please explain the example i have attached in detail for each of the steps.
    thanks much.
    Attached Thumbnails Attached Thumbnails vector example explination.-vector.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,711
    Thanks
    630
    Hello, sigma1!

    \begin{Bmatrix}\vec a &=& \overrightarrow{OA} \\<br />
\vec b &=& \overrightarrow{OB} \\ \vec c &=& \overrightarrow{OC}\end{Bmatrix} \qquad |AM| \:=\:|MB|. \qquad D \text{ is on }CM\text{ such that: }\,|CD| \:=\:2\!\cdot\!|DM|

    Code:
                  M
        A o - - - o - - - o B
          |         *   *
          |           *
          |         *   o D
          |       *       *
          |     *           *
          |   *               *
          | *                   *
        O o - - - - - - - - - - - o C

    (i)\;\text{ Find the position vector }\overrightarrow{OM} \text{ in terms of }\vec a\text{ and }\vec b.

    . . \overrightarrow{OM} \;=\;\overrightarrow{OA} + \overrightarrow{AM}

    . . \boxed{\overrightarrow{OM} \;=\;\vec a + \tfrac{1}{2}\vec b\:}




    (ii)\;\text{ Find the position vector }\overrightarrow{OD} \text{ in terms of } \vec a, \vec b, \vec c.

    \overrightarrow{OC} + \overrightarrow{CM} \;=\;\overrightarrow{OA} + \overrightarrow{AM}

    . . \vec c + \overrightarrow{CM} \;=\;\vec a + \tfrac{1}{2}\vec b

    . . . . \overrightarrow{CM} \;=\;\vec a + \tfrac{1}{2}\vec b - \vec c


    \overrightarrow{CD} \;=\;\tfrac{2}{3}\overrightarrow{CM} \;=\;\tfrac{2}{3}\left(\vec a + \tfrac{1}{2}\vec b - \vec c\right) \quad\Rightarrow\quad \overrightarrow{CD} \;=\;\tfrac{2}{3}\vec a + \tfrac{1}{2}\vec b - \tfrac{2}{3}\vec c .[1]


    \overrightarrow{OD} \;=\;\overrightarrow{OC} + \overrightarrow{CD} \;=\;\vec c + \underbrace{\left(\tfrac{2}{3}\vec a + \tfrac{1}{3}\vec b - \tfrac{2}{3}\vec c\right)}_{{\color{blue}[1]}}

    . . \boxed{\overrightarrow{OD} \;=\;\tfrac{2}{3}\vec a + \tfrac{1}{3}\vec b + \tfrac{1}{3}\vec c\:}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Jun 2009
    Posts
    806
    Thanks
    4
    i) AM = OM - OA
    MB = OB - OM.

    Since AM = MB,
    OM - OA = OB - OM.
    So.
    2OM = OA + OB
    Or
    OM = (a+b)/2.
    ii) MD = OD - OM.....(1)
    DC = OC - OD = 2MD
    MD = OC/2 - OD/2..(2)
    Equate (1) and (2)
    OD - OM = OC/2 - OD/2
    OD+OD/2 = OM + OC/2
    3OD/2 = (a+b)/2 + c/2
    OD = (a+b+c)/3
    Last edited by sa-ri-ga-ma; May 5th 2010 at 08:09 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 8
    Last Post: January 11th 2011, 10:17 AM
  2. [SOLVED] Natural log rule explination pleaseee
    Posted in the Calculus Forum
    Replies: 1
    Last Post: July 14th 2010, 06:47 PM
  3. Replies: 2
    Last Post: January 27th 2010, 08:23 PM
  4. Replies: 11
    Last Post: December 23rd 2009, 01:30 AM
  5. Replies: 2
    Last Post: October 5th 2009, 03:25 PM

Search Tags


/mathhelpforum @mathhelpforum