Question

What are the direction indices for a vector that passes from point 34 1 12 to point 14 12 1 in a cubic unit cell? please indicate negative directions by a "-" sign before the integer and omit spaces between numbers?

Answer 1

First let's rewrite both points:
 P = (34, 1, 12)
 Q = (14, 12, 1)
 From P to Q, we have:
 PQ = Q-P
 PQ = (14, 12, 1) - (34, 1, 12)
 PQ = (14-34, 12-1, 1-12)
 PQ = (-20, 11, -11)
 Rewriting:
 PQ = -20i + 11j -11k
 Answer:
 The direction indices for the vector are:
 PQ = -20i + 11j -11k