Worked example: A simple cubic lattice has a = 0.3 nm. Find the reciprocal lattice vectors and the shortest G (which labels the (100) planes). Step 1: For SC, a = a·x̂, b = a·ŷ, c = a·ẑ; V = a³. Step 2: b×c = a²x̂, so a* = (2π/a)x̂. Similarly b* = (2π/a)ŷ, c* = (2π/a)ẑ. Step 3: The reciprocal lattice is also simple cubic with spacing 2π/a = 2π/0.3 nm ≈ 20.9 nm⁻¹. Step 4: Shortest G = a* (hkl = 100), |G| = 2π/a. Bragg's law check: d₁₀₀ = a, and 2d·sinθ = λ with k′−k = G is the same condition. Conclusion: reciprocal spacing 2π/a inverts real spacing a — large real cells give finely spaced diffraction spots.