JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The sum of all possible values of \(\theta \in [0, 2\pi]\), for which the system of equations :
\(x\cos 3\theta - 8y - 12z = 0\)
\(x\cos 2\theta + 3y + 3z = 0\)
\(x + y + 3z = 0\)
has a non-trivial solution, is equal to :
- A \(\pi\)
- B \(2\pi\)
- C \(3\pi\)
- D \(4\pi\)
Answer & Solution
Correct Answer
(D) \(4\pi\)
Step-by-step Solution
Detailed explanation
For the given system of homogeneous linear equations to have a non-trivial solution, the determinant of the coefficient matrix must be zero. \(\begin{vmatrix} \cos 3\theta & -8 & -12 \\ \cos 2\theta & 3 & 3 \\ 1 & 1 & 3 \end{vmatrix} = 0\) Expanding the determinant along the…
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