If , are two non-zero and non-collinear vectors satisfying where are three distinct…

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

If x\mathbf{x} , y\mathbf{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[(a-2)\alpha^2 + (b-3)\alpha + c]\mathbf{x} + [(a-2)\beta^2 + (b-3)\beta + c]\mathbf{y} + [(a-2)\gamma^2 + (b-3)\gamma + c](\mathbf{x} \times \mathbf{y}) = 0 where α,β,γ\alpha, \beta, \gamma are three distinct real numbers, then find the value of (a2+b2+c2−4)(a^2 + b^2 + c^2 - 4) .

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