Let $$P Q R$$ be a right angled isosceles triangle, right angled at $$Q(2,1)$$. If the equation of the line $$P R$$ is $$2 x+y=3$$, then the combined equation representing the pair of lines $$P Q$$ and $$Q R$$ is

$$P S$$ 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