In lecture, we had calculated the primitive lattice vectors of a Simple cubic (SC) lattice. The reciprocal lattice vectors obtained from the calculation suggested a reciprocal space SC lattice for a direct space SC lattice. Perform a similar calculation and find the corresponding primitive reciprocal lattice vectors for the BCC and FCC direct lattice. Clearly indicate the chosen direct space lattice vectors for your calculations fo both BCC and FCC lattice. What is the resulting lattice in the reciprocal space for BCC and FCC? Note: You will receive full points only if you show all the detailed vector multiplication steps. Do not leave out any steps in the vector cross and dot product