1. The problem statement, all variables and given/known data Here's a problem I'm having: The primitive vectors of the hexagonal lattice are: a1 = ck a2 = (a/2)i + ([a√3]/2)j a3 = (-a/2)i + ([a√3]/2)j Find the primitive vectors of the reciprocal lattice, i.e. b1, b2, and b3. 2. Relevant equations I do know that the equation for b1 would be b1 = [(2*pi) (a2 X a3)] / [a1 * (a2 X a3) ] 3. The attempt at a solution I really have no idea how to do dot-products and cross-products in this case. Could someone please help me go through just the first step, which is to find b1, and then I could take it from there? Thank you very much in advance!