Take $\vec{k_{i}}$ to be the wavevector for the incoming (incident) beam and $\vec{k_{o}}$ to be the wavevector for the outgoing (diffracted) beam. $\vec{k_{o}}-\vec{k_{i}}=\Delta\vec{k}$ is the scattering vector and measures the change between the two wavevectors. Take $\vec{a_{1}},\vec{a_{2}},\vec{a_{3}}$ to be the primitive vectors of the crystal lattice. The three Laue conditions for the scattering vector, or the Laue equations, for integer values of a reflection's reciprocal lattice indices (h,k,l) can be also written as follows: