Angle between Straight Lines in Plane/General Form

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

Then the angle $\psi$ between $L_1$ and $L_2$ is given by:


 * $\tan \psi = \dfrac {l_1 m_2 - l_2 m_1} {l_1 l_2 + m_1 m_2}$

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.

Let $\psi$ be the angle between $L_1$ and $L_2$, as suggested.

Then: