Number of values of θ ∈ (0,π) for which system of linear equations x + 3y + 7z = 0 -x + 4y + 7z

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3 and 4 .Determinants and Matrices

hard

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

$1$

(JEE MAIN-2019)

Solution

$\left| {\begin{array}{*{20}{c}}
{\sin 3\theta }&{ – 1}&1\\
{\cos 2\theta }&4&3\\
2&7&7
\end{array}} \right| = 0$

$7\sin 3\theta + 14\cos 2\theta – 14 = 0$

$\sin 3\theta + 2\cos 2\theta – 2 = 0,\sin \theta = \frac{1}{2}$

Standard 12

Mathematics

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