# A Transformation Matrix question

1. May 4, 2010

1. The problem statement, all variables and given/known data

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 the origin.

2. Relevant equations

$$\left( \begin{array}{c} A'_x \\ A'_y \\ A'_z \end{array} \right) = \left( \begin{array}{ccc} R_{xx} & R_{xy} & R_{xz} \\ R_{yx} & R_{yy} & R_{yz} \\ R_{zx} & R_{zy} & R_{zz} \end{array} \right) \left( \begin{array}{c} A_x \\ A_y \\ A_z \end{array} \right)$$

3. The attempt at a solution

I am just very confused by the wording of the question. I am used to talking about the transformation of a vector... I am not sure what is being transformed here... the coordinate system?

Here is the solution:

I am having a hard time deciphering the problem statement even looking at the solution. It is clear that he wanted us to "swap" axes. But I am not sure exactly what is happening here.

2. May 4, 2010

### lanedance

you can imagine it a few different ways, i would think of it as follows:
- The global coordinate frame does not change.
- The operation is a transformation of a vector within that frame (it maps each vector to a vector).

so imagine the line from the origin to (1,1,1)

Now start with the vector (1,0,0), this will be transformed to (0,0,1).

The global co-ordinate frame doesn't change, but a vector on the x axis is mapped to a vector on the z axis.

By considering the action on each of the basis vectors it shoudl be pretty startightforward to write down the matrix.