Finding Rotational matrix from axis-angle representation

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To find the rotational matrix R from the axis-angle representation for the axis vector u=(-1, -1, -1) and an angle of pi/6, the right-hand rule is applied. The discussion highlights a concern about the accuracy of the calculations performed. A suggestion is made to test the results by applying the matrix R to the axis vector u and to a perpendicular vector to verify correctness. This testing approach can help identify any potential errors in the calculations. Ensuring the calculations align with expected outcomes is crucial for confirming the validity of the rotational matrix.
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Homework Statement


Given an axis vector u=（-1, -1, -1) , find the rotational matrix R corresponding to an angle of pi/6 using the right hand rule. Then find R(x), where x = (1,0,-1)

Homework Equations


I found the relevant equation on wikipedia (see attachment)

The Attempt at a Solution


I feel that I'm doing something wrong but I don't know what; I think I performed the calculations correctly.
upload_2014-12-3_5-9-50.png
upload_2014-12-3_5-10-6.png
upload_2014-12-3_5-9-57.png

Please help?http://blob:https%3A//www.physicsforums.com/99c786ac-ed37-4fb2-8cd5-0d1ea0a3afb5
 

Attachments

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  • upload_2014-12-3_5-9-14.png
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  • upload_2014-12-3_5-9-6.png
    upload_2014-12-3_5-9-6.png
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What makes you think something went wrong?
Have you tried testing it, i.e. by applying R to u, or to a vector perpendicular to u, and see if you get the right result?
 

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