Problem 1 (12 points) Given a crystal with the following primitive vectors: a1 = a(- + 2) a2 = a(- + y) a = az = (-8++2) where , , are unit vectors in the x,y,z directions in the Cartesian coordinate system. (a) Sketch the lattice of the crystal and identify its Bravais lattice. (b) Evaluate the volume of the primitive cell using the given primitive vectors. (c) Identify the conventional unit cell for the lattice. By counting the number of lattice points in a conventional unit cell, justify your answer in (b). (d) Identify another possible choice of the primitive vectors and calculate the volume of the primitive cell using your set of primitive vectors