1. The hexagonal Bravais lattice may be defined by the following primitive vectors: a, = (a, 0, 0), a, = (a/2, a( \\ 3)/2, 0) a; = (0, 0, c). (a) Show: the reciprocal lattice is another hexagonal lattice rotated by 30. with respect to the original one, (b) Find primitive vectors for the reciprocal lattice