##### Exercise3

Shown below in Figure 18 are the vectors $$\evec_1\text{,}$$ $$\evec_2\text{,}$$ and $$\evec_3$$ in $$\real^3\text{.}$$

1. Imagine that the thumb of your right hand points in the direction of $$\evec_1\text{.}$$ A positive rotation about the $$x$$ axis corresponds to a rotation in the direction in which your fingers point. Find the matrix definining the matrix transformation $$T$$ that rotates vectors by $$90^\circ$$ around the $$x$$-axis.

2. In the same way, find the matrix that rotates vectors by $$90^\circ$$ around the $$y$$-axis.

3. Find the matrix that rotates vectors by $$90^\circ$$ around the $$z$$-axis.
4. What is the cumulative effect of rotating by $$90^\circ$$ about the $$x$$-axis, followed by a $$90^\circ$$ rotation about the $$y$$-axis, followed by a $$-90^\circ$$ rotation about the $$x$$-axis.

in-context