If the diagonals of the parallelogram whose sides are $l x + m y + n = 0, l x + m y + n^{'} = 0$ and $m x + l y + n = 0, m x + l y + n^{'} = 0$ includes an angle $θ$ , then the value of $θ$ is

\frac{π}{3}

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\frac{π}{2}

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\frac{π}{4}

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\frac{π}{6}

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Solution

The correct option is B $\frac{π}{2}$
Distance between the parallel lines $l x + m y + n = 0, l x + m y + n^{'} = 0$ is
$\frac{| n - n^{'} |}{\sqrt{l^{2} + m^{2}}}$ units
Distance between the parallel lines $m x + l y + n = 0, m x + l y + n^{'} = 0$ is
$\frac{| n - n^{'} |}{\sqrt{l^{2} + m^{2}}}$ units

As distance between the parallel lines are equal, the parallelogram is a rhombus.
Hence, the angle between the diagonals is $\frac{π}{2} .$

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Similar questions

Q. If the diagonals of the parallelogram whose sides are

l x + m y + n = 0, l x + m y + n^{'} = 0

and

m x + l y + n = 0, m x + l y + n^{'} = 0

includes an angle

θ

, then the value of

θ

Q. Show that the diagonals of the parallelogram whose sides are

l x + m y + n = 0, l x + m y + n = 0, m x + l y + n = 0, m x + l y + n = 0

include an angle

π / 2

Q. The angle between the diagram of a parallelogram whose sides are

l x + m y + n = 0; l x + m y + n^{1} = 0; m x + l y + n = 0; m x + l y + n^{1} = 0

Q. Assertion :The diagonals of the parallelogram whose sides are

l x + m y + n = 0, l x + m y + n^{'} = 0, m x + l y + n = 0, m x + l y + n^{'} = 0

are perpendicular. Reason: If the perpendicular distances between parallel sides of a parallelogram are equal, then it is a rhombus.

Show that the diagonals of the parallelogram whose sides are $l x + m y + n = 0$ , $l x + m y + n^{^{'}} = 0$ , $m x + l y + n = 0$ and $m x + l u + n^{^{'}} = 0$ include an angle $\frac{π}{2}$

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If the diagonals of the parallelogram whose sides are lx+my+n=0,lx+my+n′=0 and mx+ly+n=0,mx+ly+n′=0 includes an angle θ, then the value of θ is

If the diagonals of the parallelogram whose sides are $l x + m y + n = 0, l x + m y + n^{'} = 0$ and $m x + l y + n = 0, m x + l y + n^{'} = 0$ includes an angle $θ$ , then the value of $θ$ is