Primitive lattice vectors, reciprocal lattice, wigner seitz cell

solas99
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How can i develop a sketch of the lattice and reciprocal lattice from vector form

a=i+4j
b=3i

i know how to draw the wigner site cell, but I am having problems developing a sketch from vectors.
what is the method for working it out..please help
 
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I have one question.
Why for construct reciprocal lattice we must exchange non-bravies lattice to a bravies lattice?
 

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