Alright, let’s walk through this step by step like I’m right here with you! ### **Step 1: Find the Intercepts** The plane **pqr** cuts the axes at: - x-axis at \( p = 2a \) - y-axis at \( r = 3a/4 \) - z-axis at \( q = a \) ### **Step 2: Write Intercepts as Fractions of ‘a’** - x: \( 2a \) → \( 2 \) - y: \( 3a/4 \) → \( 3/4 \) - z: \( a \) → \( 1 \) ### **Step 3: Take Reciprocals** - x: \( 1/2 \) - y: \( 4/3 \) - z: \( 1 \) ### **Step 4: Clear Fractions (Find LCM and Multiply)** The common denominator for 2 and 3 is 6. So, multiply all reciprocals by 6: - x: \( (1/2) \times 6 = 3 \) - y: \( (4/3) \times 6 = 8 \) - z: \( 1 \times 6 = 6 \) ### **Step 5: Write Miller Indices** Write the answer in parentheses, no commas: **(3 8 6)** --- **Final Answer:** **The Miller indices are (3 8 6).** Let me know if you want a quick check of the steps or have any follow-up!