Eq(2.16) can be expressed in terms of components. Setting
we have
which is known as the Cartesian equation for the plane. An alternative form is
where
Eq(2.19) is called a linear equation in x, y and z. In general, a linear equation in R^{3} represents a plane and vice versa.
Two planes with parallel normal vectors are said to be parallel to each other.
Thus, the planes
are parallel.
Two planes are orthogonal if their normal vectors are orthogonal.
More generally, the angle between 2 planes is defined as the angle between their normal vectors.