Let S be the set of all values of \theta \in[-\pi, \pi] for which the system of linear equations x+y+\sqrt{3} z=0 -x+(\tan \theta) y+\sqrt{7} z=0 x+y+(\tan \theta) z=0 has non-trivial solution. Then \frac{120}{\pi} \sum_{\theta \in S} \theta is equal to [8-Apr-2023 shift 2]

Matrices and Determinants Part 3

Section: Mathematics

Question : 49 of 100

Marks: +1, -0

Let S be the set of all values of θ∈[−π,π] for which the system of linear equations
‌x+y+√3z=0
‌−x+(tan‌θ)y+√7z=0
‌x+y+(tan‌θ)z=0
has non-trivial solution. Then ‌

120

‌

∑

θ∈S

θ is equal to

[8-Apr-2023 shift 2]

Validate

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1	1	√3
−1	tan‌θ	√7
1	1	tan‌θ