With usual notations, in any $$\triangle A B C$$, if $$a\cos B=b \cos A$$, then the triangle is

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\mathrm{a}=1$$, then measure of angle $$\mathrm{A}=$$

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio.

In a triangle $$A B C$$ with usual notations, if $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$, then area of triangle $$A B C$$ with $$a=\sqrt{6}$$ is