If the line $$l_{1}: 3 y-2 x=3$$ is the angular bisector of the lines $$l_{2}: x-y+1=0$$ and $$l_{3}: \alpha x+\beta y+17=0$$, then $$\alpha^{2}+\beta^{2}-\alpha-\beta$$ is equal to _________.

Let the equations of two adjacent sides of a parallelogram $$\mathrm{ABCD}$$ be $$2 x-3 y=-23$$ and $$5 x+4 y=23$$. If the equation of its one diagonal $$\mathrm{AC}$$ is $$3 x+7 y=23$$ and the distance of A from the other diagonal is $$\mathrm{d}$$, then $$50 \mathrm{~d}^{2}$$ is equal to ____________.

The equations of the sides AB, BC and CA of a triangle ABC are : $$2x+y=0,x+py=21a,(a\pm0)$$ and $$x-y=3$$ respectively. Let P(2, a) be the centroid of $$\Delta$$ABC. Then (BC)$$^2$$ is equal to ___________.

The equations of the sides $$\mathrm{AB}, \mathrm{BC}$$ and $$\mathrm{CA}$$ of a triangle $$\mathrm{ABC}$$ are $$2 x+y=0, x+\mathrm{p} y=15 \mathrm{a}$$ and $$x-y=3$$ respectively. If its orthocentre is $$(2, a),-\frac{1}{2}<\mathrm{a}<2$$, then $$\mathrm{p}$$ is equal to ______________.