# Plane

A plane can be represented in 2 forms: scalar form and normal form.

#### Scalar Equation of Plane in $R_{3}$

$π:ax+by+cz=d$ The normal vector $n= abc $

#### Vector Form of the Plane

$π:x= x_{1}⋮x_{n} =OP+su+tvs,t∈R$ where $u,v$ are non-zero non-parallel vectors. Intuitively, there is a unique plane that goes across two lines that are not parallel.

The normal vector $n=u×v$