Let's determine the Miller indices for planes A and B step by step. ### **Step 1: Identify the intercepts of each plane with the axes (in terms of the lattice constant a)** **For Plane A:** From the diagram, Plane A cuts the x-axis at 1, y-axis at 1/2, and z-axis at 1/3. **For Plane B:** Plane B cuts the x-axis at 1, y-axis at 1, and z-axis at 1/2. ### **Step 2: Write the intercepts as (x, y, z)** For Plane A, the intercepts are (1, 1/2, 1/3). For Plane B, the intercepts are (1, 1, 1/2). ### **Step 3: Take reciprocals of the intercepts** For Plane A: Reciprocals are (1/1, 1/(1/2), 1/(1/3)) = (1, 2, 3). For Plane B: Reciprocals are (1/1, 1/1, 1/(1/2)) = (1, 1, 2). ### **Step 4: Clear fractions (if any) by multiplying with the lowest common multiple (LCM) to get whole numbers** For both planes, the reciprocals are already whole numbers. ### **Step 5: Write Miller indices as (hkl)** For Plane A, the Miller indices are (1 2 3). For Plane B, the Miller indices are (1 1 2). ### **Final Answers** Plane A has Miller indices (1 2 3). Plane B has Miller indices (1 1 2).