A cube has corners with coordinates (0, 0, 0), (1, 0, 0), (0, 1, 0), (1, 1, 0), (0, 0, 1), (1, 0, 1), (0, 1, 1) and (1, 1, 1). Find the vectors representing the diagonals of the cube and hence find the length of the diagonals and the angle between the diagonals.