$$x, y, z$$ are in G.P. and $$\tan ^{-1} x, \tan ^{-1} y, \tan ^{-1} z$$ are in A.P., then

In $$\triangle A B C$$ with usual notation, $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$ and $$a=\frac{1}{\sqrt{6}}$$, then the area of triangle is _______ sq. units.

If $$\hat{\mathrm{a}}$$ and $$\hat{\mathrm{b}}$$ are unit vectors and $$\overline{\mathrm{c}}=\hat{\mathrm{b}}-(\hat{\mathrm{a}} \times \overline{\mathrm{c}})$$, then minimum value of $$[\hat{a} \hat{b} \bar{c}]$$ is

Angles of a triangle are in the ratio $$4: 1: 1$$. Then the ratio of its greatest side to its perimeter is