If a 2 + b 2 + c 2 = 1, then | array ccc a^ 2 + (b^ 2 +c^ 2 ) & b(1- ) & a(1- ) a(1- ) &…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If a2 + b2 + c2 = 1, then
\[\left|\begin{array}{ccc} a^{2}+\left(b^{2}+c^{2}\right) \cos \phi & b(1-\cos \phi) & a(1-\cos \phi) \\ a(1-\cos \phi) & b^{2}+\left(c^{2}+a^{2}\right) \cos \phi & b(1-\cos \phi) \\ a(1-\cos \phi) & b(1-\cos \phi) & c^{2}+\left(a^{2}+b^{2}\right) \cos \phi \end{array}\right|\]
is independent of
\[\left|\begin{array}{ccc} a^{2}+\left(b^{2}+c^{2}\right) \cos \phi & b(1-\cos \phi) & a(1-\cos \phi) \\ a(1-\cos \phi) & b^{2}+\left(c^{2}+a^{2}\right) \cos \phi & b(1-\cos \phi) \\ a(1-\cos \phi) & b(1-\cos \phi) & c^{2}+\left(a^{2}+b^{2}\right) \cos \phi \end{array}\right|\]
is independent of
- a
- b
- c
- φ
Answer
(A) a, (B) b, (C) c
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