If →x,→y are two non-zero and non-collinear vectors satisfying [(a−2)α2+(b−3)α+c]→x+[(a−2)β2+(b−3)β+c]→y+[(a−2)γ2+(b−3)γ+c](→x×→y)=→0, where α,β,γ are three distinct real numbers, then which of the following statement(s) is/are correct ?

If →x,→y are two non-zero and non-collinear vectors satisfying [(a

1.	If →x,→y are two non-zero and non-collinear vectors satisfying [(a−2)α2+(b−3)α+c]→x+[(a−2)β2+(b−3)β+c]→y+[(a−2)γ2+(b−3)γ+c](→x×→y)=→0, where α,β,γ are three distinct real numbers, then which of the following statement(s) is/are correct ?
Answer» If $\to x, \to y$ are two non-zero and non-collinear vectors satisfying $[(a - 2) α^{2} + (b - 3) α + c] \to x + [(a - 2) β^{2} + (b - 3) β + c] \to y + [(a - 2) γ^{2} + (b - 3) γ + c] (\to x \times \to y) = \to 0,$ where $α, β, γ$ are three distinct real numbers, then which of the following statement(s) is/are correct ?