If \( \alpha, \beta, \gamma \) are the angles of a triangle and the system of equations \[ \begi...

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If \( \alpha, \beta, \gamma \) are the angles of a triangle and the system of equations
\[
\begin{array}{l}
\cos (\alpha-\beta) x+\cos (\beta-\gamma) y+\cos (\gamma-\alpha) z=0 \\
\cos (\alpha+\beta) x+\cos (\beta+\gamma) y+\cos (\gamma+\alpha) z=0 \\
\sin (\alpha+\beta) x+\sin (\beta+\gamma) y+\sin (\gamma+\alpha) z=0
\end{array}
\]
has non-trivial solutions, then triangle is necessarily
(a) Equilateral
(b) Isosceles
(c) Right angled
(d) Acute angled
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