The acute angle between the lines $y = 3$ and $y = \sqrt{3}x + 9$ is .....$^o$

Show that two lines $a_{1}x + b_{1}y + c_{1} = 0$ and $a_{2}x + b_{2}y + c_{2} = 0$,where $b_{1}, b_{2} \neq 0$,are perpendicular if $a_{1}a_{2} + b_{1}b_{2} = 0$.

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

The acute angle between two straight lines passing through the point $M(-6, -8)$ and the points in which the line segment $2x + y + 10 = 0$ enclosed between the coordinate axes is divided in the ratio $1 : 2 : 2$ in the direction from the point of its intersection with the $x$-axis to the point of intersection with the $y$-axis is:

The distance of a point $(2, 5)$ from the line $3x + y + 4 = 0$ measured along the lines $L_1$ and $L_2$ are the same. If the slope of line $L_1$ is $\frac{3}{4}$,then the slope of the line $L_2$ is

Find the equation of the line passing through the point $(3, -2)$ and making an angle of $60^{\circ}$ with the line $\sqrt{3}x + y = 1$.