The Miller indices of the direction shown in the figure are……………a.[102]b.[012]c.[210]d.[120]

To determine the Miller indices for the specified direction, we will go through the following steps:

1. ### Break Down the Problem

Identify the direction indicated in the figure and extract the necessary coordinates. Miller indices are derived from these coordinates.

2. ### Relevant Concepts

Miller indices represent crystal directions in a three-dimensional lattice. The indices [hkl] can be found based on the direction vector's coordinates (x, y, z).

3. ### Analysis and Detail

Assuming the figure provides a direction vector $\vec{v} = (x, y, z)$:

• Determine the integers $h, k, l$ from the coordinates.
• Normalize the direction, if necessary, to its simplest integer form.

(As the figure is not provided, I will proceed with the assumption of determining the indices based on four provided options.)

4. ### Verify and Summarize

Check each option against potential direction combinations:

• Option a: [102]
• Option b: [012]
• Option c: [210]
• Option d: [120]

Final Answer

Please provide the coordinates depicted in the figure to correctly assign the Miller indices to the direction. Without the visual reference, I cannot choose the correct indices from the listed options.