Determine the lattice vectors a, b and c of the primitive unit cell for the face-centred cubic lattice in terms of cartesian unit vectors i, j and k. assume the cube has side length a. (b) prove that the cell bounded by your vectors is a primitive cell. (c) assume that there is a single spherical atom at each lattice point of the foc lattice, and that these atoms pack the volume as densely as possible (close-packed). determine the fraction of volume that is occupied by "atoms” in this structure. (note, this is called the packing fraction.)