If $\overrightarrow a, \overrightarrow b, \overrightarrow c,$are unit vectors such that $\overrightarrow a + \overrightarrow b + \overrightarrow c = \overrightarrow 0$, find the value of $\overrightarrow a ⋅ \overrightarrow b + \overrightarrow b ⋅ \overrightarrow c + \overrightarrow c ⋅ \overrightarrow a$.
$\begin{array}{1 1}(A) \frac{1}{\sqrt 2} (a^2+b^2+c^2)\\(B) \frac{-1}{\sqrt 2}(a^2+b^2+c^2) \\ (C) \frac{1}{ 2}(a^2+b^2+c^2) \\ (D) \frac{-1}{ 2}(a^2+b^2+c^2) \end{array}$