Vector Rotation: How to Rotate a Vector by 90 Degrees using a Rotation Matrix

[_Andreas]

Homework Statement

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

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?

 

[tiny-tim]

Hi _Andreas!

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

erm … not enough sleep? …

Hint: try multiplying by -1 ​

 

[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: $$\vec{y}=\begin{pmatrix} -x_2 \\ x_1 \end{pmatrix}=-x_2 \hat{e_1} + x_1 \hat{e_2}$$

 

[_Andreas]

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: $$\vec{y}=\begin{pmatrix} -x_2 \\ x_1 \end{pmatrix}=-x_2 \hat{e_1} + x_1 \hat{e_2}$$

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