(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the 3 × 3 matrix A such that its transform is the 120 degrees rotation inR3about the axis through the origin and the point (1, 1, 1).

2. Relevant equations

Rotation Matrix inR2:

R = (cosx, -sinx

sinx, cosx)

3. The attempt at a solution

My idea is that since every rotation about an axis lies in a plane that is perpendicular to that axis, then I could simply find an orthogonal basis with dim = 2 to generate a plane parallel to the rotation plane (i.e. with the normal vectorn= (1,1,1) ), followed by the next three procedures:

1)Project the point in question onto the plane (obtaining thus the coordinates of the transformed point relative to the plane's basis).

2)Rotate the projected point on the plane by 120 degrees by using the regularR2rotation matrix.

3)Apply the inverse of the projection matrix to what I got from part (2), so that the rotated point on the plane is projected back ontoR3.

If the operators to project and rotate are P, R respectively, then the required transform is

[tex] T = P^{-1}RP[/tex]

Now this sounds like a lot of work, and there could be a better solution (hopefully), which is what I would really like to see. Thanks for any help.

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# Homework Help: Rotation about axis in R3

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