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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant

જો \(\alpha+\beta+\gamma=2 \pi\) તો સમીકરણ સંહતિ  \(x+(\cos \gamma) y+(\cos \beta) z=0\)  ;  \((\cos \gamma) x+y+(\cos \alpha) z=0\)  ; \((\cos \beta) x+(\cos \alpha) y+z=0\) નો ઉકેલગણ . . .  ..

  1. A ખાલીગણ
  2. B અનંત ઉકેલ ધરાવે
  3. C માત્ર બેજ ઉકેલ ધરાવે
  4. D એક્જ ઉકેલ ધરાવે
Verified Solution

Answer & Solution

Correct Answer

(B) અનંત ઉકેલ ધરાવે

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Detailed explanation

\(\alpha+\beta+\gamma=2 \pi\) \(\left|\begin{array}{ccc}1 & \cos \gamma & \cos \beta \\ \cos \gamma & 1 & \cos \alpha \\ \cos \beta & \cos \alpha & 1\end{array}\right|\) \(=1+2 \cos \alpha \cdot \cos \beta \cdot \cos \gamma-\cos ^{2} \alpha-\cos ^{2} \beta-\cos ^{2} \gamma\)…
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