Finding Miller indexes of a vector vertical to known layer

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To find the Miller indices of a vector perpendicular to the layer with indices (211), one must first understand that Miller indices represent the orientation of a crystal plane. The approach of inverting the indices to obtain coordinates is incorrect, as Miller indices describe planes, not vectors. A more appropriate method involves determining the normal vector to the plane defined by the Miller indices. Clarification on Miller indices and their application in crystallography may help in understanding the relationship between layers and their corresponding vectors. Understanding these concepts is essential for accurately solving the problem.
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Homework Statement


Find Miller indexes of the vector that is vertical to the layer (211).

Homework Equations


Unknown.

The Attempt at a Solution


I'm not quite sure how to do this. The only thing I came up until now is to invert the numbers (so that I get 1/2, 1 and 1) and then find the vector that is vertical to a vector with these coordinates. But I don't think this is right at all, because this is a layer we are talking about. Not a vector.
 
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Sollicitans said:
I'm not quite sure how to do this. The only thing I came up until now is to invert the numbers (so that I get 1/2, 1 and 1) and then find the vector that is vertical to a vector with these coordinates. But I don't think this is right at all, because this is a layer we are talking about. Not a vector.

your above statement is not clear to me -why not ask a question :
What are Miller indexes in an array of atoms/crystalline arrangements ?
 

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