I don't know if this is the right section, but this problem is in my electromagnetism course (Griffiths text).(adsbygoogle = window.adsbygoogle || []).push({});

This is problem 1.9 of Griffiths (3rd edition) text: Find the transformation matrix R that describes a rotation by 120 degrees about an axis from the origin through the point (1,1,1). The rotation is clockwise as you look down the axis toward origin.

At first, I didn't understand the question (actually I still think I don't understand it). But then I read a book on vectors and tensors that I used as a reference in my vector analysis course last year. I couldn't come up with a solution even then. So I discussed it with a friend.

We came up with the following solution: (phi=120degrees)

(cos phi sin phi) = (-0.5 0.866)

(-sin phi cos phi) (-0.866 -0.5)

I am sorry I can't present it in LaTeX as I am not experienced, but there are square matrices on boths sides of the equation.

But isn't this ridiculously simple? This just tells of rotation of 120 degrees about a certain axis (say x-axis). It doesn't say anything about a new axis coming from origin to point (1,1,1). What more should I do?

A friend put the two components Ay, Az both equal to 1. Multiplied this column vector with the rotation matrix I wrote above, and came up with the value of Ay(prime) and Az(prime). His values were:

Ay(prime)=0.366

Az(prime)=-1.366

But this gives the value of coordinates, not the rotation matrix itself. The question asks for the rotation matrix!

I simply don't understand what I should do with this question. This is basically a chapter on vector analysis, and I have almost done all other questions except this one. This one has been bothering me for days now. I have no idea if my solution is right. I don't even know why the question specifically mentions an axis through (1,1,1), if it only required me to put rotation angle, phi, equal to 120degree!

Any help will be greatly appreciated.

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# Transformation Matrix Problem

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