Geometry

I've been stuck on a question for an hour, I'm really bad at proving things... so I would really appreciate any help that you can give me on this question.

Basically, there are three axis at 120 degrees to each other pointing away from the origin. If you draw a line through two of the axis, it will intersect the third axis. If h, k and i are the reciprocals of the fractional intercepts of the axis. The intercepts of the first two axis determine the intercept of the third axis, therefore the value of i depends on that of h and k with the relation

h + k = -i

I've been asked to prove that equation.

>.<

After using the cosine rule twice on a drawing I worked out (probably incorectly) that

y^2 + xy - 3x^2 = 4z(z-y)


Where x y and z are the intercepts of the axis a1 a2 and a3 respectivly. I probably went down the wrong road by choosing general intercept points as opposed to general miller indicies (repciprocal of the fractional intercepts).


Its hard to explain the question, ask if you don't understand what I typed. Or read "elements of xray diffraction" chapter 2.

Draw a sketch in Paint (or something similar) and send it as an attachment. That will make it easier to understand

Maybe a picture from the page would help:

http://woof82.co.uk/media/pictures/photos/vectors.jpg

I'm to prove equation 2-2