The angle between the straight lines $3x + 4y + 9 = 0$ and $x - 7y - 22 = 0$ is

If $A(-3,3), B(1,1), C(1,-1)$ and $D(-2,-2)$ are the vertices of a quadrilateral,the angle between the diagonals $AC$ and $BD$ is

$A$ line $L$ passes through the point $(3, -2)$ and is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y = 1$. If $L$ also intersects the $x$-axis,then the equation of $L$ is:

If the equation of a line having a slope $m$ $(m \in \mathbb{Z})$,passing through $(1, 1)$ and making an angle of $\tan^{-1}\left(\frac{5}{7}\right)$ with the line $x + y - 3 = 0$ is $ax + y + c = 0$,then $ac =$

The equations of the lines passing through the point $(3,2)$ which make an angle of $45^{\circ}$ with the line $x-2y=3$ are

If the line $(2x + 3y + 4) + \lambda(6x - y + 12) = 0$ is perpendicular to the line $7x + 5y = 2$,then $\lambda = $