Question:
Determine the Miller indices for the plane intersecting the coordinate axes \(x=2\), \(y=2\), and \(z=3\).
Determine the Miller indices for the plane intersecting the coordinate axes \(x=2\), \(y=2\), and \(z=3\).
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For Miller indices, take reciprocals of intercepts and multiply by LCM to get integers.
Updated On: May 19, 2026
- \((3\ 3\ 2)\)
- \((2\ 2\ 3)\)
- \((1\ 1\ 0)\)
- \((0\ 0\ 1)\)
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The Correct Option is A
Solution and Explanation
Concept:
Miller indices are obtained by taking reciprocals of intercepts and then clearing fractions.
Step 1: Write the intercepts. \[ x=2,\quad y=2,\quad z=3 \] So, intercepts are: \[ (2,2,3) \]
Step 2: Take reciprocals. \[ \left(\frac{1}{2},\frac{1}{2},\frac{1}{3}\right) \]
Step 3: Clear fractions.
LCM of \(2,2,3\) is \(6\). \[ \left(\frac{1}{2}\times6,\frac{1}{2}\times6,\frac{1}{3}\times6\right) \] \[ (3,3,2) \] \[ \therefore \text{Correct Answer is (A)} \]
Miller indices are obtained by taking reciprocals of intercepts and then clearing fractions.
Step 1: Write the intercepts. \[ x=2,\quad y=2,\quad z=3 \] So, intercepts are: \[ (2,2,3) \]
Step 2: Take reciprocals. \[ \left(\frac{1}{2},\frac{1}{2},\frac{1}{3}\right) \]
Step 3: Clear fractions.
LCM of \(2,2,3\) is \(6\). \[ \left(\frac{1}{2}\times6,\frac{1}{2}\times6,\frac{1}{3}\times6\right) \] \[ (3,3,2) \] \[ \therefore \text{Correct Answer is (A)} \]
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