Problem 1: There is a rot-inversion symmetry \(\bar{3}\) along z axis [0 0 1] and intercepting with the origin (x=0, y = 0, z=0). For a position with Cartesian coordinate (x = 2.0 Ã…, y = 1.0 Ã…, z = 1.0 Ã…), what are the Cartesian coordinates for all its symmetry-equivalent points (Here we use right-hand rotation axis for \(\bar{3}\), which means anti-clockwise rotation in the following projection figure)