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If a + b + c = 0 and a 2 + b 2 + c 2 - a b - b c - c a ≠ 0 , ∀ a , b , c ∈ R , then the system of equations a x + b y + c z = 0 , b x + c y + a z = 0 and c x + a y + b z = 0 has

Options

  1. AA unique solution
  2. BInfinite solutions
  3. CNo solution
  4. DExactly two solutions

Correct answer

B. Infinite solutions

Step-by-step solution

Note that a b c b c a c a b = - a + b + c 2 a - b 2 + b - c 2 + c - a 2 Since, D = 0 & 0,0 , 0 is a solution, hence the system has infinite solutions.

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