JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of values of \(\theta \in (0,\pi)\) for which the system of linear equations
\(x + 3y + 7z = 0\)
\(-x + 4y + 7z = 0\)
\((sin\,3\theta )x + (cos\,2\theta )y + 2z = 0\) has a non-trivial solution, is
- A \(3\)
- B \(2\)
- C \(4\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\left| {\begin{array}{*{20}{c}} {\sin 3\theta }&{ - 1}&1\\ {\cos 2\theta }&4&3\\ 2&7&7 \end{array}} \right| = 0\) \(7\sin 3\theta + 14\cos 2\theta - 14 = 0\) \(\sin 3\theta + 2\cos 2\theta - 2 = 0,\sin \theta = \frac{1}{2}\)
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