Find the angle between the lines $y - \sqrt{3}x - 5 = 0$ and $\sqrt{3}y - x + 6 = 0$. (in $^{\circ}$)

$A$ 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:

The equations of the lines passing through the point $(3,2)$ and making an acute angle of $45^{\circ}$ with the line $x-2y-3=0$ are

To which of the following types do the straight lines represented by $2x + 3y - 7 = 0$ and $2x + 3y - 5 = 0$ belong?

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:

If $m=1$ is the slope of a line $L$,then the product of the slopes of non-parallel lines which are inclined at an angle of $60^{\circ}$ with $L$ is