In a triangle ABC, a $$-$$ 2b + c = 0. The value of $$\cot \left( {{A \over 2}} \right)\cot \left( {{C \over 2}} \right)$$ is

Consider the following statements :

Statement I

If the line segment joining the points P(m, n) and Q(r, s) subtends an angle $$\alpha$$ at the origin, then $$\cos \alpha = {{ms - nr} \over {\sqrt {({m^2} + {n^2})({r^2} + {s^2})} }}$$.

Statement II

In any triangle ABC, it is true that $${a^2} = {b^2} + {c^2} - 2bc\cos A$$.

Which one of the following is correct in respect of the above two statements?

What is the area of the triangle with vertices $$\left( {{x_1},{1 \over {{x_1}}}} \right),\left( {{x_2},{1 \over {{x_2}}}} \right),\left( {{x_3},{1 \over {{x_3}}}} \right)$$ ?

In a $$\Delta$$ABC, if a = 2, b = 3 and $$\sin A = {2 \over 3}$$, then what is $$\angle$$B equal to?