If `a, b, c, x, y, z in R` such that `ax + by + cz = 2`, then which of the following is always true

Let S={z in C:z(iz_(1)+1,|z_(1)| lt 1} . Then, for all z in S , which one of the following is always true?

a/(y-z) = b/(z-x) = c/(x-y) then ax + by + cz =___

If pqrne0 and the system of equations (p + a) x + by + cz = 0 , ax + (q + b)y + cz = 0 ,ax + by + (r + c) z =0 has a non-trivial solution, then value of (a)/(p) + (b)/(q) + (c )/(r ) is a)-1 b)0 c)1 d)2

If a^2+b^2+c^2 =16, x^2+y^2+z^2 = 25 and ax+by+cz = 20 , then show that (a+b+c) prop (x+y+z)

If x, y, z are in A.P.; ax, by, cz are in GP. and 1/a, 1/b, 1/c are in A.P., then x/z+z/x is equal to