Condition for Straight Lines in Plane to be Perpendicular/General Equation

Theorem
Let $L_1$ and $L_2$ be straight lines embedded in a cartesian plane, given in general form:

Then $L_1$ is perpendicular to $L_2$ :


 * $l_1 l_2 + m_1 m_2 = 0$

Proof
From the general equation for the straight line:

Hence the slope of $L_1$ and $L_2$ are $-\dfrac {l_1} {m_1}$ and $-\dfrac {l_2} {m_2}$ respectively.

From Condition for Straight Lines in Plane to be Perpendicular: Slope Form we have:

$-\dfrac {l_1} {m_1} = \dfrac {m_2} {l_2}$

from which the result follows.