The equation of a line making an angle $60^{\circ}$ with the line $x+y-3=0$ and passing through the point $(1,1)$ is

If $\theta$ is the acute angle between the lines $\frac{x}{a}+\frac{y}{b}=1$ and $\frac{x}{b}+\frac{y}{a}=1$,then $\sin \theta=$

The angle between the lines $2x - y + 5 = 0$ and $3x + y + 4 = 0$ is ...$^o$.

The acute angle between the line $4x - 2y + 13 = 0$ and the line which makes equal intercepts with the coordinate axes is

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 $m_1 + m_2 =$

Let $\theta_1$ be the angle between two lines $2x + 3y + c_1 = 0$ and $-x + 5y + c_2 = 0$,and $\theta_2$ be the angle between two lines $2x + 3y + c_1 = 0$ and $-x + 5y + c_3 = 0$,where $c_1, c_2, c_3$ are any real numbers.
Statement-$1$: If $c_2$ and $c_3$ are proportional,then $\theta_1 = \theta_2$.
Statement-$2$: $\theta_1 = \theta_2$ for all $c_2$ and $c_3$.