(Solution) - In the graphite picture imagine that we are interested in -(2025 Original AI-Free Solution)

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In the graphite picture, imagine that we are interested in a point 5:67 Ångstroms over and 3:14 Ångstroms up from the origin.
(a) Express that point in terms of the basis given for graphite.
(b) How many hexagonal shapes away is this point from the origin?
(c) Express that point in terms of a second basis, where the first basis vector is the same, but the second is perpendicular to the first (going up the plane) and of the same length.