Equation of Planes
Implicit Form
A plane can be given by implicit equation
(this is called the scalar equation of planes)
or alternatively the scalar triple product
(where
Derivation
To derive the above equation, we can use a normal vector
Alternatively, given three points
Importance in Multi-variable Calculus
Equation of planes is important in multi-variable calculus since when we go closer and closer to a surface, it can be approximated by a plane.
Parametric Form
A plane can also be expressed parametrically by a base point