Let A and B denote the statements \[ \] A: $ \cos \alpha + \cos \beta + \cos \gamma = 0$ \[\] B: $ \sin \alpha + \sin \beta + \sin \gamma = 0$ \[\] If $ \cos(\beta- \alpha) + \cos( \gamma- \alpha) + \cos( \alpha - \beta)= -\large\frac{3}{2}$, then

Question

$\begin {array} {1 1} (A)\;A\: is \: true\: and\: B\: is\: false & \quad (B)\;A \: is\: false\: and\: B\: is\: true \\ (C)\;Both\: A\: and\: B\: are\: true & \quad (D)\;Both\: A \: and \: B \: are\: false \end {array}$