Deduce primitive lattice vectors from position vector.

  1. 1. The problem statement, all variables and given/known data
    given the following position vector:

    R = (10n1 + 9n2 + 19n3)(a/10) x + 6(n2+n3)(a/5) y + 2(n3)a z

    where n1, n2 and n3 are integers
    Find the primitive lattice vectors.

    2. Relevant equations
    any position vector of a lattice point is of the type
    R= c1 a1 + c2 a2 + c3 a3;
    and a position vector like the one showed above is a linear combination of the primitive lattice vectors a1, a2 and a3.

    3. The attempt at a solution

    I think I solved the question correctly, but my intuition tells me its wrong:

    we can do the following:
    a1 = a/10 X
    a2 = a/5 Y
    a3 = a Z

    In our case, since n1,n2 and n3 are just integers:

    c1 = 10n1 + 9n2 + 19n3
    c2 = 6(n2 + n3)
    c3 = 2n3
  2. jcsd
  3. Any hint in the right direction is helpful?
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