The values of $\theta, \lambda$ for which the following equations $\sin \theta x - cos\theta y + (\lambda +1)z = 0$; $\cos\theta x + \sin\theta\, y - \lambda z = 0$;$ \lambda x +(\lambda + 1)y + \cos\theta z = 0$ have non trivial solution, is
The values of $\theta, \lambda$ for which the following equations $\sin \theta x - cos\theta y + (\lambda +1)z = 0$; $\cos\theta x + \sin\theta\, y - \lambda z = 0$;$ \lambda x +(\lambda + 1)y + \cos\theta z = 0$ have non trivial solution, is
- A
$\theta = n\pi , \lambda \in R - {0}$
- B
$\theta = 2n\pi , \lambda $ is any rational number
- C
$\theta = (2n + 1)\pi , \lambda \in R+, n \in I$
- D
$\theta = (2n + 1),\frac{\pi }{2} \lambda \in R, n \in I$
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- [AIEEE 2004]