vectors

{\left|a - b \right|}^2 + {\left|b - c \right|}^2 + {\left|c - a \right|}^2 = |a|^2 + |b|^2 - 2\hat{a}\hat{b} + |b|^2 + |c|^2 - 2\hat{b}\hat{c} + ..... = 6 - 2(\hat{a}\hat{b} + \hat{b}\hat{c} + \hat{c}\hat{a}) = 6 - 2(cos\alpha + cos\beta + cos\gamma)

Since the max value of the expression in brackets is 1 + 1 + 1 = 3 and minimum is -3, this expression doesn't exceed 12?
Actually its range becomes [0, 12] I think..