The diagonals of the parallelogram whose sides are $lx + my + n = 0,$ $lx + my + n' = 0$,$mx + ly + n = 0$, $mx + ly + n' = 0$ include an angle
$\frac{\pi }{3}$
$\frac{\pi }{2}$
${\tan ^{ - 1}}\left( {\frac{{{l^2} - {m^2}}}{{{l^2} + {m^2}}}} \right)$
${\tan ^{ - 1}}\left( {\frac{{2lm}}{{{l^2} + {m^2}}}} \right)$
Let $PQR$ be a right angled isosceles triangle, right angled at $P\, (2, 1)$. If the equation of the line $QR$ is $2x + y = 3$, then the equation representing the pair of lines $PQ$ and $PR$ is
The $x -$ co-ordinates of the vertices of a square of unit area are the roots of the equation $x^2 - 3 |x| + 2 = 0$ and the $y -$ co-ordinates of the vertices are the roots of the equation $y^2 - 3y + 2 = 0$ then the possible vertices of the square is/are :
The vertices of $\Delta PQR$ are $P (2,1), Q (-2,3)$ and $R (4,5) .$ Find equation of the median through the vertex $R$.
The area of the triangle bounded by the straight line $ax + by + c = 0,\,\,\,\,(a,b,c \ne 0)$ and the coordinate axes is