A zone axis is a lattice row parallel to the intersection of two (or more) families of lattices planes. It is denoted by [ u v w ]. A zone axis [ u v w ] is parallel to a family of lattice planes of Miller indices ( hkl ) if: \[uh + vk + wl = 0 \nonumber \] This is the so-called Weiss law. The indices of the zone axis defined by two lattice planes ( h 1 , k 1 , l 1 ), ( h 2 , k 2 , l 2 ) are given by: \[\frac{u}{\begin{vmatrix} k_1 &l_1 \\ k_2 &l_2 \end{vmatrix}}=\frac{v}{\begin{vmatrix} l_1 &h_1 \\ l_2 &h_2 \end{vmatrix}}=\frac{w}{\begin{vmatrix} h_1 &k_1 \\ h_2 &k_2\\ \end{vmatrix}} \nonumber \] Conversely, any crystal face can be determined if one knows two zone axes parallel to it. It is the zone law, or Zonenverbandgesetz . Three lattice planes have a common zone axis ( are in zone ) if their Miller indices ( h 1 , k 1 , l 1 ), ( h 2 , k 2 , l 2 ), ( h 3 , k 3 , l 3 ) satisfy the relation: \[\begin{vmatrix} h_1 & k_1 & l_1\\h_2 & k_2 & l_2\\h_3 & k_3 & l_3\\\end{vmatrix}=0 \nonumber \]