As illustrated in the diagram below, the angle between two planes
and
is equal to the angle between the normals to the planes
and
The components of the normal appear in the cartesian equation of the plane, because if
is any point in the plane,
is any fixed point and the normal is
then
where
and
are the position vectors of
and
respectively. This results in the equation of the plane
and the normal can be read off:
Thus given the cartesian equations of two planes, we can read off the normals
and
and the angle between the planes is given by
Example: Planesandare given by
and
The normalsandare given by
and
