How do I find the reciprocal primitive vector for a lattice?

[delrepublica]

Homework Statement

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.

Homework Equations

I do know that the equation for b1 would be

b1 = [(2*pi) (a2 X a3)] / [a1 * (a2 X a3) ]

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!

 

[delrepublica]

please help!

 

[delrepublica]

anybody??

 

[malawi_glenn]

why don't you know how to do dot and cross products? What is the problem? Can you show us?

there is no need to post twice "please help" and "anybody"... calm down, and show attempt to solution.

I mean how would YOU do to find b1?