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

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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, A unique solution, Infinite solutions, No solution, Exactly two solutions

MARKS App · Accepted Answer

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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