Problem 3. The schematic figure below shows a face-centered cubic (FCC) lattice with a lattice constant of a. 1. Draw the lattice vectors of a primitive unit cell for the FCC lattice. Also write them in equation form (e.g. a1=nx^+my^+lz^, where x^=xx is the unit vector in the x direction). (0.5 points) 2. Derive an expression for the reciprocal lattice vectors of an FCC lattice. (1.5 points) 3. Using these sets of reciprocal lattice vectors, draw (or generate) the reciprocal lattice of FCC in reciprocal space. Show that this reciprocal lattice is equivalent to a body-centered cubic lattice with a lattice constant of a4(0.5 points )