# How to form the transformation matrix for this

1. Aug 27, 2015

### Byang

We were asked to form the transformation matrix that rotates the x1 axis of a rectangular coordinate system 60 degrees toward x2 and the x3 axis.
The thing is, I don't understand what it meant by rotating one axis toward the two other. Like, do I rotate x1 60 degrees toward the x2-x3 plane or does it mean something else? I tried to rotate x1 to the x2-x3 plane but I can never be sure of the angle between x1' and x2, and x1' and x3. How do I find the angles?

2. Aug 27, 2015

### Ray Vickson

There are infinitely many possible ways of rotating the $x_1$ axis by $60^o$ towards the $x_2-x_3$ plane. For example, you could fix $x_2 = 0$ and rotate the $x_1$ axis towards the $x_3$ axis, or fix $x_3 = 0$ and rotate $x_1$ towards $x_2$, etc. In all these cases you would be rotating $x_1$ by $60^o$ towards the $x_2-x_3$ plane. In general, you could fix an arbitrary point $p = (0,p_2,p_3)$ in the $x_2-x_3$ plane, and rotate the $x_1$ axis towards $p$.

Basically, I don't know exactly what your question wants; perhaps they mean $60^o$ towards $x_2$ and then $60^o$ towards $x_3$, or maybe they mean two separate questions---one for an $x_1 \to x_2$ rotation and another for an $x_1 \to x_3$ rotation.

3. Aug 28, 2015

### Byang

Haha, that's exactly my problem. But thank you for answering. We've cleared it up with our teacher and she said it was supposed to be "around x3 axis," which makes the problem a lot easier.

4. Aug 31, 2015

### Staff: Mentor

Thread moved as it seems to be more of a general question than a specific homework problem.