Final answer:
The Miller indices (3 0 2) define a crystallographic plane, whereas [3 0 2] signifies a crystallographic direction in a simple cubic crystal system. The plane intersects the x-axis at 1/3 and the z-axis at 1/2, while the direction moves along the lattice 3 units right and 2 units forward.
Step-by-step explanation:
The question involves interpreting Miller indices for a simple cubic crystal system. The Miller indices (3 0 2) define a crystallographic plane, while the notation [3 0 2] represents a crystallographic direction within the lattice.
In a simple cubic system, each lattice point is located only at the corners of the cubic unit cell. For understanding the plane (3 0 2), one can visualize it as intersecting the x-axis at 1/3, having an infinite intersection with the y-axis (since the Miller index is 0), and intersecting the z-axis at 1/2. The direction [3 0 2], on the other hand, indicates a direction that proceeds right 3 units, up 0 units (staying in the same plane), and forward 2 units.