The two lines lx + my = n and l'x + m'y = n' | vedclass

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(A) The equation of the first line is $lx + my = n$,which can be written as $y = -\frac{l}{m}x + \frac{n}{m}$. The slope $m_1 = -\frac{l}{m}$.The equa

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$ll' + mm' = 0$

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(A) The equation of the first line is $lx + my = n$,which can be written as $y = -\frac{l}{m}x + \frac{n}{m}$. The slope $m_1 = -\frac{l}{m}$.The equation of the second line is $l'x + m'y = n'$,which can be written as $y = -\frac{l'}{m'}x + \frac{n'}{m'}$. The slope $m_2 = -\frac{l'}{m'}$.Two lines are perpendicular if the product of their slopes is $-1$,i.e.,$m_1 	imes m_2 = -1$.$\left(-\frac{l}{m}ight) 	imes \left(-\frac{l'}{m'}ight) = -1$$\frac{ll'}{mm'} = -1$$ll' = -mm'$$ll' + mm' = 0$.

The two lines $lx + my = n$ and $l'x + m'y = n'$ are perpendicular if

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