If the points $(1, 2)$ and $(3, 4)$ lie on opposite sides of the line $3x - 5y + a = 0$,then:

If the line $x-y+1=0$ cuts the lines $2x+2y+3=0$ and $3x+3y+2=0$ at the points $A$ and $B$ respectively,then $AB=$

The equation of the base of an equilateral triangle is $x + y = 2$ and the vertex is $(2, -1)$. The length of the side of the triangle is

Find the length of the perpendicular drawn from the origin to the line $\frac{x}{a} + \frac{y}{b} = 1$.

$O(0,0), B(-3,-1), C(-1,-3)$ are vertices of a triangle $OBC$. $D$ is a point on $OC$ and $E$ is a point on $OB$. If the equation of $DE$ is $2x + 2y + \sqrt{2} = 0$,then the ratio in which the line $DE$ divides the altitude of the triangle $OBC$ from $O$ to $BC$ is:

Find the distance between the lines $3x + 2y + 7 = 0$ and $6x + 4y + 3 = 0$.