Equation of Wavefront of Plane Wave/Direction Cosine Form

Theorem
Let $\phi$ be a plane wave.

Let an arbitrary wavefront of $\phi$ be denoted $P$.

Let the direction of propagation of $\phi$ be expressed as:
 * $x : y : z = l : m : n$

where $l$, $m$ and $n$ are the direction cosines of the normal to $P$.

Then:
 * $l x + m y + n z = K$

where $K$ is constant for a given plane wave $\phi$.