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Vector - sum of two vectors * some const

  1. Feb 4, 2008 #1
    a*<3, 2> + b*<-2, 3> = <2, 3> - A, B?

    1. The problem statement, all variables and given/known data
    There exists a vector <2, 3>.
    Said vector is the sum of two other vectors <3, 2> and the orthoginal to <3,2> (which I think is <-2, 3> right?)


    2. Relevant equations
    <2, 3> = a<3, 2> + b<-2, 3> where a, b are constants


    3. The attempt at a solution
    I tried solving the x and y seperately: 2 = a*3 + b*-2 but there's many ways this can be done, none of which held true also for the y.
     
    Last edited: Feb 4, 2008
  2. jcsd
  3. Feb 4, 2008 #2
    Maybe I didn't describe it well enough. The problem is that I have a vector <2, 3> and I must get from the origin to (2, 3). I start moving parallel to <3, 2> and make a right angle turn. Where do I make the right angle turn?
     
  4. Feb 4, 2008 #3
    EDIT:
    I take back the above matrix, which I am now deleting. The system you'll need to solve is

    [tex]
    \begin{align*}
    2x + 3y &= 13\\
    2x - 3y &= 0
    \end{align*}
    [/tex]

    Which can be solved via elimination.
     
    Last edited: Feb 4, 2008
  5. Feb 4, 2008 #4
    Well, I just tried elimination using gaussian elimination

    Code (Text):

    Starting matrix:
    2  3    13
    2 -3    0

    to
    2  3    13
    0 -6   13

    to
    1  3/2    13/2
    0  1      13/-6

    to
    1  0    39/4
    0  1    13/-6
     
    so I end up with x = 39/4 and y=13/-6
    But I asked and he told me that it wasn't correct.
     
  6. Feb 5, 2008 #5
    Has he given you the correct answer? Maybe I don't understand the question completely.
     
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