The acute angle between the lines $x \cos 30^{\circ} + y \sin 30^{\circ} = 3$ and $x \cos 60^{\circ} + y \sin 60^{\circ} = 5$ is (in $^{\circ}$)

The distance between the two points $A$ and $A'$ which lie on $y = 2$ such that both the line segments $AB$ and $A'B$ (where $B$ is the point $(2, 3)$) subtend an angle $\frac{\pi}{4}$ at the origin,is equal to

The angle between the lines $x \cos \alpha_1 + y \sin \alpha_1 = p_1$ and $x \cos \alpha_2 + y \sin \alpha_2 = p_2$ is

The obtuse angle between the lines $y = -2$ and $y = x + 2$ is .....$^o$

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

$A$ 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: