If $\;\hat{x} , \hat{y}\;$ and $\;\hat{z}\;$ are three unit vectors in three - dimensional space , then the minimum value of $\;|\hat{x} + \hat{y}|^{2} + |\hat{y} + \hat{z}|^{2} + |\hat{z} + \hat{x}|^{2}\;$ :

Question

$(a)\;\large\frac{3}{2} \qquad(b)\;\normalsize 3\qquad(c)\;\normalsize 3 \sqrt{3}\qquad(d)\;6$