$$P S$$ is the median of the triangle with vertices at $$P(2,2), Q(6,-1)$$ and $$R(7,3)$$, then the intercepts on the coordinate axes of the line passing through point $$(1,-1)$$ and parallel to PS are respectively

If the angle between the lines given by $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0 ; \lambda \geq 0$$ is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then the value of $$\lambda$$ is

The base of an equilateral triangle is represented by the equation $$2 x-y-1=0$$ and its vertex is $$(1,2)$$, then the length (in units) of the side of the triangle is

A line is drawn through the point $$(1,2)$$ to meet the co-ordinate axes at $$\mathrm{P}$$ and $$\mathrm{Q}$$ such that it forms a $$\triangle \mathrm{OPQ}$$, where $$\mathrm{O}$$ is the origin. If the area of $$\triangle \mathrm{OPQ}$$ is least, then the slope of the line $$\mathrm{PQ}$$ is