I've been banging my head against this problem for some time now, and I just can't solve it. The problem seems fairly simple, but for some reason I don't get it.(adsbygoogle = window.adsbygoogle || []).push({});

Given the coordinate transformation matrix

[tex]A=\left( \begin{array}{ccc}\cos{\alpha}&0&-\sin{\alpha}\\0&1&0\\\sin{\alpha}&0&\cos{\alpha}\end{array}\right)[/tex]

show how

[tex]\mathbf{B}=\mathbf{r} \times \hat{z}[/tex]

transforms. Now how do I do this? For example, I've tried writing out the cross product, which becomes

[tex]\mathbf{B} = -y\hat{x} + x\hat{y}[/tex]

and then simply transforming this vector using the above matrix A, but it doesn't seem to work.

Any hints on how to think about this?

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# Homework Help: Orthogonal transformation

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