Equation of a Plane
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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
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Sources
- Seth Warner: Modern Algebra (1965): $\S 28$
