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

  • A

    $\frac{\pi }{3}$

  • B

    $\frac{\pi }{2}$

  • C

    ${\tan ^{ - 1}}\left( {\frac{{{l^2} - {m^2}}}{{{l^2} + {m^2}}}} \right)$

  • D

    ${\tan ^{ - 1}}\left( {\frac{{2lm}}{{{l^2} + {m^2}}}} \right)$

Similar Questions

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

A rod of length eight units moves such that its ends $A$ and $B$ always lie on the lines $x-y+2=0$ and $y+2=0$, respectively. If the locus of the point $P$, that divides the $\operatorname{rod} AB$ internally in the ratio $2: 1$ is $9\left(x^2+\alpha y^2+\beta x y+\gamma x+28 y\right)-76=0$, then $\alpha-\beta-\gamma$ is equal to :

  • [JEE MAIN 2025]