If ` vec x , vec y` are two non-zero and non-collinear vectors satisfying `[(a-2)alpha^2+(b-3)alpha+c] vec x+[(a-2)beta^2+(b-3)beta+c] vec y+[(a-2)gamma^2+(b-3)gamma+c]( vec xxx vec y)=0, w h e r ealpha,beta,gamma` are three distinct real numbers, then find the value of `(a^2+b^2+c^2-4)dot`