Answer:
THE PROPER EXPLANATION IS BELOW:
Step-by-step explanation:
We can use the crystal structure together to plan a direction in the cubic unit cell. In this system, the x, y, and z axes are aligned along the edges of the cubic unit cell.
(a)[110]: Starts at origin (0, 0, 0) and moves along the positive x-axis until it reaches (1, 0, 0) point. Then, traverse the positive y-axis until the point (1, 1, 0) is reached. Finally, move along the positive z-axis until the point (1, 1, 1) is reached.
This direction passes through the center of the two opposite faces of the cubic unit cell.
(b)[121]: Starts at origin (0, 0, 0) and moves along the positive x-axis until reaching (1, 0, 0) point. Then, traverse the positive y-axis until point (1, 2, 1) is reached. Finally, move along the positive z-axis until point (1, 2, 2) is reached. This direction passes through the corners of the two adjacent faces of the cubic unit cell.
(c) [112]:
Start at starting point (0, 0, 0) and move along the positive x-axis until point (1, 0, 0) is reached. Then, traverse the positive y-axis until the point (1, 1, 0) is reached. Finally, move along the positive z-axis until point (1, 1, 2) is reached. This direction passes through the space between two opposite points of the cubic unit cell.
Note that these illustrations represent instructions in the cubic unit cell and do not represent the unit cell itself.