Nonzero non-collinear vectors x , y satisfy ( a α 2 + b α + c ) x + ( a β 2 + b β + c ) y + ( a γ 2 + bγ + c ) ( x × y ) = 0 , where α , β , γ are distinct and a , b , c ∈ R . Then a + b + c is

Question

Nonzero non-collinear vectors x , y ​ satisfy ( a α 2 + b α + c ) x + ( a β 2 + b β + c ) y ​ + ( a γ 2 + bγ + c ) ( x × y ​ ) = 0 , where α , β , γ are distinct and a , b , c ∈ R . Then a + b + c is

TestHub · Accepted Answer

The three vectors are linearly independent, so the quadratic a t 2 + b t + c has three distinct roots. It is identically zero; hence a = b = c = 0 .

Mathematics - Vector Question with Solution | TestHub

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