If a = 1044, b = 1047, c = 1041, then find a2 + b2 + c2 - ab - bc - ca.

27 30 26 12

27

a2 + b2 + c2 - ab - bc - ca = \(\frac{1}{2}\) [(a - b)2 + (b - c)2 + (c - a)2]                                        = \(\frac{1}{2}\) [(1044 - 1047)2 + (1047 - 1041 )2 + (1041 - 1044)2]                                        = \(\frac{1}{2}\) [9 + 36 + 9] = 27