1.
If x⃗\vec{x} and y⃗\vec{y} are two non-zero, non-collinear vectors satisfying ((a−3)α2+(b−4)α+(c−1))x⃗+((a−3)β2+(b−4)β+(c−1))y⃗+((a−3)γ2+(b−4)γ+(c−1))(x⃗×y⃗)=0⃗((a-3)\alpha^2+(b-4)\alpha+(c-1))\vec{x} + ((a-3)\beta^2+(b-4)\beta+(c-1))\vec{y} + ((a-3)\gamma^2+(b-4)\gamma+(c-1))(\vec{x}\times\vec{y}) = \vec{0} (where α,β,γ\alpha, \beta, \gamma are three distinct numbers), then a2+b2+c24\frac{a^2+b^2+c^2}{4} rounded off to the nearest integer is