- #1
Gregg
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- 0
Homework Statement
The matrix
[itex] \left[ \begin{array}{ccc} 0 &1 &0 \\ 0 &0 &1 \\ 1 &0 &0 \end{array} \right] [/itex]
represents a rotation.
(a) Find the equation of the axis of this rotation.
(b) What is the angle of the rotation?
Homework Equations
[itex]\left[ \begin{array}{ccc} 1 &0 &0 \\ 0 &\cos\theta &-\sin\theta \\ 0 &\sin\theta &\cos\theta \end{array} \right] [/itex]
[itex] \left[ \begin{array}{ccc} \cos\theta &0 &\sin\theta \\ 0 &1 &0 \\ -\sin\theta & 0 &\cos\theta \end{array} \right] [/itex]
[itex]\left[ \begin{array}{ccc} \cos\theta &-\sin\theta &0 \\ \sin\theta &\cos\theta &0 \\ 0 &0 &1 \end{array} \right] [/itex]
Rotations of \theta about x, y and z axes respectively.
The Attempt at a Solution
I thought this would just be a case of looking at the matrix and deciding whether it was a rotation about the x,y or z. I'm not sure how to determine the equation for the axis of rotation.
I discovered that:
[itex] \left[ \begin{array}{ccc} 0 &1 &0 \\ 0 &0 &1 \\ 1 &0 &0 \end{array} \right] \left[ \begin{array}{ccc} x_1 &x_2 &x_3 \\ y_1 &y_2 &y_3 \\ z_1 &z_2 &z_3 \end{array} \right] = \left[ \begin{array}{ccc} y_1 &y_2 &y_3 \\ z_1 &z_2 &z_3 \\ x_1 &x_2 &x_3 \end{array} \right] [/itex]
But can't get close to the answer.