Finding Hexagonal Crystalline Directions

[Seiayyi]

Homework Statement

What are the Miller-Bravais indices for the direction represented by the vector that has been drawn within a unit cell?

Homework Equations

u = 1/3(2u' - v')
v = 1/3(2v' - u')
t = -(u+v)
w = w'

Equations from this book: Materials Science & Engineering an Introduction by Callister, 8th Edition

The Attempt at a Solution

From the image, I got that the values of a1, a2, and c are respectively: 1/2, 1/2, 1/2. Then multiplying by 2 to get integer values, I have u'=1, v'=1, and w'=1. Working everything out with the given equations, I from that the direction should be [11-23] but my answer turned out to be wrong.

I'm not sure if I'm interpreting the image incorrectly or if I'm not using the equations correctly.

 

[Seiayyi]

Hello?