Equation of Plane

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Theorem

A plane $P$ is the set of all $\tuple {x, y, z} \in \R^3$, 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