JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If the system of equations \( x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \) \( x+(\cos \alpha) y+(\sin \alpha) z=0 \) \( x+(\sin \alpha) y-(\cos \alpha) z=0\) has a non-trivial solution, then \(\alpha \in\left(0, \frac{\pi}{2}\right)\) is equal to :
- A \(\frac{3 \pi}{4}\)
- B \(\frac{7 \pi}{24}\)
- C \(\frac{5 \pi}{24}\)
- D \(\frac{11 \pi}{24}\)
Answer & Solution
Correct Answer
(C) \(\frac{5 \pi}{24}\)
Step-by-step Solution
Detailed explanation
\(\left|\begin{array}{ccc}1 & \sqrt{2} \sin \alpha & \sqrt{2} \cos \alpha \\ 1 & \sin \alpha & -\cos \alpha \\ 1 & \cos \alpha & \sin \alpha\end{array}\right|=0\) \( \Rightarrow 1-\sqrt{2} \sin \alpha(\sin \alpha+\cos \alpha)+\sqrt{2} \cos \alpha(\cos \alpha-\sin \alpha)=0 \)…
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