A crystal is composed of atoms, molecules or ions that are arranged in a repetitive manner, forming a three-dimensional space lattice. Each point in the space lattice represents either a particle or a collection of particles (known as a basis), and a set of lattice points can be connected by a plane. As there are many possible ways to connect lattice points with planes of different orientations, a system is needed to define these planes. We begin by deriving the vector and scalar equations of a plane.

*P(x, y, z)* and *P _{0}(x_{0}, y_{0}, z_{0})* are two points on a plane with position vectors

**and**

*r**respectively, which makes*

**r**_{0 }**–**

*r**the vector from*

**r**_{0 }*P*to

_{0 }*P*. The plane has a direction defined by the normal vector

*, which is perpendicular to the vector*

**n**(A, B, C)**–**

*r**. Therefore,*

**r**_{0}where *D = Ax _{0} + By_{0} + Cz_{0}*.

Eq1 is the vector equation of a plane, while eq2 is the scalar equation of a plane, where *D/A*, *D/B* and *D/C* are the intercepts of the plane with the *x*-axis, *y-*axis and *z*-axis respectively.