Question

Show that the planes (100), (010), and (001) do not belong to the same family of planes in a
hexagonal lattice. Write the Miller-Bravais indices for each of these planes.

Answer 1

I think this belongs in the mathematics section, not chemistry.

Answer 2

This is definitely a chemistry thing. It's used for determining crystal structures with x-ray crystalography. I don't remember how to do it though I'm afraid since I didn't really get too deep into it. But I think what he has there are the planes of a cubic and a hexagonal will have something like this:

Answer 3

I have never worked with x-ray crystallography before.