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

If the lines $y = (2 + \sqrt{3})x + 4$ and $y = kx + 6$ are inclined at an angle of $60^{\circ}$ to each other,then the value of $k$ will be

The angle between the line joining the points $(1, -2)$ and $(3, 2)$ and the line $x + 2y - 7 = 0$ is

The lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ are perpendicular to each other,if

If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin,then the absolute value of the product of all possible values of $a$ is:

$A$ straight line $L$ through the point $(3,-2)$ 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