Vector rotation

1. Nov 30, 2008

_Andreas

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?

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• Rotationsmatris.jpg
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2. Nov 30, 2008

tiny-tim

Hi _Andreas!
erm … not enough sleep?

Hint: try multiplying by -1

3. Nov 30, 2008

gabbagabbahey

What you've drawn for your rotated vector is $x_1 \hat{e_1} - x_2 \hat{e_2}$; which is not the same as what you calculated using the transformation matrix: $$\vec{y}=\begin{pmatrix} -x_2 \\ x_1 \end{pmatrix}=-x_2 \hat{e_1} + x_1 \hat{e_2}$$

4. Nov 30, 2008

_Andreas

Thanks! I did suspect that this was the case, but I wasn't sure.