Create an array, permutation

Hello, I have (a, b, c) i want to get ((a-b)^2, (b-c)^2, (c-a)^2) My goal is to maximize dot product of (1/6,1/3,1/2)*((a-b)^2,(b-c)^2,(c-a)^2) So i want to permute (1/6,1/3,1/2) find max value of dot product to choose best weights for (a,b,c)