If $A (-2, 1)$,$B (2, 3)$,and $C (-2, -4)$ are three points,then what is the angle between $BA$ and $BC$?

If the two lines $\frac{3}{2} x + (2a - 1)y = 3$ and $2x + a^2y = -3$ are perpendicular,then the distance of their point of intersection from the point $(1, 1)$ is

Find the angle between the lines joining the points $(0, 0), (2, 3)$ and $(2, -2), (3, 5)$.

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 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

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 $c_3$.