A straight line parallel to the line $y=\sqrt{3} x$ passes through $Q(2,3)$ and cuts the line $2 x+4 y-27=0$ at $P$. Then, the length of the line segment $P Q$ is

If a line $a x+2 y=k$ forms a triangle of area 3 sq. units with the coordinate axis and is perpendicular to the line $2 x-3 y+7=0$, then the product of all the possible values of $k$ is

The orthocenter of the triangle whose sides are given by $x+y+10=0, x-y-2=0$ and $2 x+y-7=0$ is

For $l \in R$, the equation $(2 l-3) x^2+2 l x y-y^2=0$ represents a pair of distinct lines