If the three lines $2x + y = 4$,$3x + 2y = 3$,and $ax + 3y = 2$ are concurrent,find the value of $a$.

$(x_1, y_1)$ is the point of concurrency of a family of lines. If the algebraic sum of the lengths of the perpendiculars drawn to these lines from $(2, 0)$,$(0, 2)$,and $(1, 1)$ is zero,then $(x_1, y_1) =$

If the lines $3x + y - 2 = 0$,$px + 2y - 3 = 0$,and $2x - y - 3 = 0$ are concurrent,then $p =$

Find the value of $p$ so that the three lines $3x + y - 2 = 0$,$px + 2y - 3 = 0$,and $2x - y - 3 = 0$ intersect at a single point.

The equation of a line passing through the point of intersection of the lines $x + 5y + 7 = 0$ and $3x + 2y - 5 = 0$,and perpendicular to the line $7x + 2y - 5 = 0$,is given by

The distance between the points of concurrency of the two families of straight lines given by $x+(5 \lambda+1) y+1-3 \lambda=0$ and $(5 \mu+2) x-3 y+3+6 \mu=0$ is