Main Concept

The equation of a plane in ${\mathrm{\ℝ}}^3$ can be given as

$A x \+ B y \+ C z \= D$

where A, B, C, D are parameters.

The normal vector to the plane with the above equation is the vector $\left(A\, B\, C\right)$.

Two planes ${\mathrm{\π}}_{1 }$and ${\mathrm{\π}}_2$ are perpendicular when their respective normals $n_{1 }$and $n_2$ are perpendicular:

$n_{1 }\cdot n_2 \= 0$

Two planes ${\mathrm{\π}}_{1 }$and ${\mathrm{\π}}_2$ are parallel when their respective normals $n_{1 }$and $n_2$ are parallel:

$n_1\times n_2\=0$

More MathApps

MathApps/NaturalSciences