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Homework Help: Vector rotation

  1. Nov 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Rotate a vector v=x_1e_1+x_2e_2 90 degrees by using the rotation matrix.

    3. The attempt at a solution

    As you can see in the attached image, I get a 90 degree clockwise rotation. I'm supposed to get a 90 degree counterclockwise rotation. Where do I go wrong?
     

    Attached Files:

  2. jcsd
  3. Nov 30, 2008 #2

    tiny-tim

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    Hi _Andreas! :smile:
    erm … not enough sleep? :redface:

    Hint: try multiplying by -1 :smile:
     
  4. Nov 30, 2008 #3

    gabbagabbahey

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    What you've drawn for your rotated vector is [itex]x_1 \hat{e_1} - x_2 \hat{e_2}[/itex]; which is not the same as what you calculated using the transformation matrix: [tex]\vec{y}=\begin{pmatrix} -x_2 \\ x_1 \end{pmatrix}=-x_2 \hat{e_1} + x_1 \hat{e_2}[/tex]
     
  5. Nov 30, 2008 #4
    Thanks! I did suspect that this was the case, but I wasn't sure.
     
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