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

Question

$\begin{array}{1 1}(a)\;A\;is \;false\;and \;B\;is \;true\\(b)\;Both\; A \;and \;B\;are\;true\\(c)\;Both\;A\;and \;B\;are\;false\\(d)\;A\;is\; true\;and\;B\;is \;false\end{array}$