1.9 A sequence of two rotations is required to locate uniquely the axis of a vehicle or body. Consider the sequence $\psi$, $\theta$ as shown. The first rotation is through angle $\psi$ about X, followed by a rotation through $\theta$ about $\eta$. The overall transformation is
$\begin{bmatrix} x \\ y \\ z \end{bmatrix} = \alpha \begin{bmatrix} X \\ Y \\ Z \end{bmatrix}$
(a) Determine the elements of matrix $\alpha$.
(b) Test for orthogonality by taking $\alpha^{-1}$.
(c) If a vector has components x = 0, y = 2, z = 0, determine its components in the X, Y, Z frame.