We use the results :
\(\overline{b} \times \overline{b} = 0\) and if in a scalar triple product, two vectors are equal, then the scalar triple product is zero.

Alternative Method :

\(\therefore \overline{c}\) is a linear combination of \(\overline{a}\) and \(\overline{b}\)
\(\therefore\) \(\overline{a}\), \(\overline{b}\), \(\overline{c}\) are coplanar
\(\therefore\) [\(\overline{a}\) \(\overline{b}\) \(\overline{c}\)] = 0.