If \( \sin \beta \neq \cos \beta \) and \( x, y \) and \( z \) sati...

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If \( \sin \beta \neq \cos \beta \) and \( x, y \) and \( z \) satisfy the equations
\[
\begin{array}{c}
x \cos \alpha-y \sin \alpha+z=\cos \beta+1 \\
x \sin \alpha+y \cos \alpha+z=-\sin \beta+1 \\
x \cos (\alpha+\beta)-y \sin (\alpha+\beta)+z=2
\end{array}
\]
then \( x^{2}+y^{2}+z^{2} \) equals
(a) 1
(b) 2
(c) 3
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