Crystallographic Directions

This is the 1st portion of a lecture covering crystallographic directions and planes within metallic and ceramic crystal structures. This is from Chapter 3 of the Principles of Engineering Materials Course (ET 2300) at Ohio University
This video is time-stamped as follows:
Introduction 0:00
Finding Miller Indices for Vectors 10:00
Miller Indices Exercise - Graphical Method 19:05
Miller Indices Exercise - Mathematical Method 22:33
Sketching Vectors from Miller Indices 25:20
Calculating Linear Density 33:01

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[@orensavir]

I have a question about the last example,
The constant relations you gave for the different crystals are for the most dense linear vectors ( BCC = 111), but the vector asked about is actually in the 110 vector, so why did you take the radius to edge correlation of sqrt3 and not sqrt2
??
Thank you

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