Within a cubic unit cell, sketch the following directions: (a) [101] (e) \([\overline{1} 1 \overline{1}]\) (b) [211] (f) \([\overline{2} 12]\) (c) \([10 \overline{2}]\) (g) [3\overline{12} ] (d) \([3 \overline{13}]\) (h) [301]

Answer: To sketch the given directions, follow these steps: 1. Understand the direction integers that represent movements along the x, y, and z axis. 2. Sketch the direction (a) [101] by moving 1 unit in the x direction, 0 units in the y direction, and 1 unit in the z direction. 3. Sketch the direction (e) [-111] by moving -1 unit in the x direction, 1 unit in the y direction, and -1 unit in the z direction. 4. Sketch the direction (b) [211] by moving 2 units in the x direction, 1 unit in the y direction, and 1 unit in the z direction. 5. Sketch the direction (f) [-212] by moving -2 units in the x direction, 1 unit in the y direction, and 2 units in the z direction. 6. Sketch the direction (c) [10-2] by moving 1 unit in the x direction, 0 units in the y direction, and -2 units in the z direction. 7. Sketch the direction (g) [3-12] by moving 3 units in the x direction, -1 unit in the y direction, and 2 units in the z direction. 8. Sketch the direction (d) [3-13] by moving 3 units in the x direction, -1 unit in the y direction, and 3 units in the z direction. 9. Sketch the direction (h) [301] by moving 3 units in the x direction, 0 units in the y direction, and 1 unit in the z direction.