How to Find Intercept with Axis for Miller Indices?

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To find intercepts with axes for Miller indices, one must determine the coordinates for the given directions in 3D space. The discussion includes attempts to calculate the indices for two directions, with initial values provided for both. Clarifications were made regarding the terminology, noting that "x, y, z components" is the standard term in American English, while "indices" is used in British English. The use of the Pythagorean theorem was suggested for justifying distances in calculations. Overall, the conversation revolves around understanding how to accurately represent and calculate Miller indices in three-dimensional geometry.
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Homework Statement



for direction 1 and 2, find the indexes x y z for both

Homework Equations



n/a

The Attempt at a Solution



direction 1 is 0,0.25,0.3 ?
direction 2 is 0,-0.3,0.25 ?
 

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What is the definition of an index?
 
icantadd said:
What is the definition of an index?

the direction [x,y,z]
 
Okay, I see the pic now. You are starting from the origin. Just calculate where the point is in the table.
 
icantadd said:
Okay, I see the pic now. You are starting from the origin. Just calculate where the point is in the table.

I'm not quite really sure if I get this right since it is in 3D and is very confusing.

Now, I have Direction 1 [0, 0.25, 0.3]

Direction 2 [0.4, 0.25, -0.3]

Would you please verify if what I have looks good?

Thank you in advance
 
Yeah, now it looks good. If you need to justify the distances, ue pythagoras theorem.
 
icantadd said:
Yeah, now it looks good. If you need to justify the distances, ue pythagoras theorem.

Alright, thank you very much for your clarifications.
 
The standard English term is "x, y, z components" not "indices". In "British English", the letters "x", "y", "z" in, say, u_x, u_y, or u_z would be "indices" (in "American English", "subscripts").
 
hi,can anybody tell how to find intercept with axis for miller indices?
 
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