If the two lines $7x + 3y + 9 = 0$ and $y = kx + 7$ are perpendicular to each other,find the value of $k$.

The slope of a line $L$ is $2$. If $m_1$ and $m_2$ are the slopes of two lines which are inclined at an angle of $\frac{\pi}{6}$ with $L$,then $m_1 + m_2 =$

If the two lines $\frac{3}{2} x + (2a - 1)y = 3$ and $2x + a^2y = -3$ are perpendicular,then the distance of their point of intersection from the point $(1, 1)$ is

The acute angle between the lines $x-3=0$ and $x+y=19$ is: (in $^{\circ}$)

If the lines $2x + 3ay - 1 = 0$ and $3x + 4y + 1 = 0$ are mutually perpendicular,then the value of $a$ will be

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