The angle between the diagram of a parallelogram whose sides are $l x + m y + n = 0; l x + m y + n^{1} = 0; m x + l y + n = 0; m x + l y + n^{1} = 0$ is

π / 3

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π / 2

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\frac{π}{4}

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π / 6

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Solution

The correct option is B $π / 2$
A] Consider,
$l x + m y + n = 0$
$\Rightarrow m y = - l x - n$
$∴ y = - \frac{l}{m} x - \frac{n}{m}$
consider
$l x + m y + n^{1} = 0$
$\Rightarrow y = - \frac{l}{m} x - \frac{n^{1}}{m}$
$A B = | n^{1} - n |$ $B C = | n^{1} - n |$
$C D = | n^{1} - n |$ $A D = | n^{1} - n |$
all sides are equal
$∴$ it is a square
Hence diagonals of a square are $⊥^{1}$ as
to each other so angle is $\frac{π}{2}$

Suggest Corrections

Similar questions

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

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 $\frac{π}{2}$

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. 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. 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.

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The angle between the diagram of a parallelogram whose sides are lx+my+n=0; lx+my+n1=0; mx+ly+n=0; mx+ly+n1=0 is

The correct option is B π/2A] Consider,lx+my+n=0⇒my=−lx−n∴y=−lmx−nmconsiderlx+my+n1=0⇒y=−lmx−n1mAB=|n1−n| BC=|n1−n|CD=|n1−n| AD=|n1−n|all sides are equal ∴ it is a square Hence diagonals of a square are ⊥1 as to each other so angle is π2

The angle between the diagram of a parallelogram whose sides are $l x + m y + n = 0; l x + m y + n^{1} = 0; m x + l y + n = 0; m x + l y + n^{1} = 0$ is