Find the transformation matrix that rotates a rectangular coordinate system through an angle of 120 degrees about an axis making equal angles with the original three coordinate axes.

Question

perl · Answer

are you given which axis it rotates about?

anonymous · Answer

This is the whole problem

anonymous · Answer

If you can I'd like some insight into how to prepare transformation matrices involved in rotating, I've never been good at it

legends · Answer

Sorry I dont know:(

anonymous · Answer

I'm aware that there are formulas but a more general one is tough to find

anonymous · Answer

Well, i never faced the subject. After doing some reading I found the following document that briefly goes through it: http://physics.ucf.edu/~lc/3323_RT.pdf You can see problem 1.9 at the second page. The exact question there is: "Find the transformation matrix R that describes a rotation by 120° about an axis from the origin through the point (1,1,1). The rotation is clockwise." However that axis has the same angle with any one of the original axis. So it seems to be the same question in a little different version. Hope it helps =)

anonymous · Answer

So does this mean I can assume we are spinning about one axis? Because I was unclear about that. And in which case that makes this much easier.

anonymous · Answer

Yes the spinning is done on a single axis. The 'new' axis.
Since the angles between the 'new' axis and the original axes are equal, it means that if you'd imagine looking from the direction of this new axis onto your original system you'd see something like this:
|dw:1423806101159:dw|
Which mean that from that direction the angle between the axes 'seems' $120^\circ$.
So by intuition that means the axis will simply substitute. z will become x, x will become y and y become z. and that's what their matrix does.