Let ABC be a triangle and a, b and  $c$  are length of the sides, opposite to vertices A, B and  $C$ respectively. If $\overrightarrow{\alpha }$   and   $\overrightarrow{\beta }$  are two non collinear unit vectors satisfying
$(\text{a}-\text{b})\overrightarrow{\alpha }+(\text{b}-\text{c})\overrightarrow{\beta }+(\text{c}-\text{a})(\overrightarrow{\alpha }\times \overrightarrow{\beta })=\overrightarrow{0}.$ Then which of the following is/are True for $\Delta \text{ABC}$?