Hi everyone, to find the draw the direction for a given miller index say,  we first convert this miller index consisting of 4 indices into one containing 3 indices. To do so, we have a set of formulae prescribed in almost every book. Sadly I haven't been able to come across a single book the gives the derivation of those formulae! I thought that i could use vector-component method to get the results but that gives totally weird formulae not even close to the ones i see in my textbooks. (have a look at the attached image) So, can anyone suggest me a textbook, a link or anything that can help me understand the derivation? I'm not finding the enthusiasm for rote-memorising the formulae if i don't know where they come from... Thanks!