# Equation of Plane

## Theorem

A plane $P$ is the set of all $\left({x, y, z}\right) \in \R^3$, where:

- $\alpha_1 x + \alpha_2 y + \alpha_3 z = \gamma$

where $\alpha_1, \alpha_2, \alpha_3, \gamma \in \R$ are given, and not all of $\alpha_1, \alpha_2, \alpha_3$ are zero.

## Proof

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 28$