$($a$)$ For a hexagonal closed packed $($hcp$)$ structure with an axial ratio of $1\mathrm{.}633$ and atomic

diameter of $2\mathrm{.}8,$ calculate the linear density of atoms along the $011$ direction.

$($b$)$ The unit cell of a cubic crystal structure has a lattice parameter of $2\mathrm{.}5.$ If the Miller

indices of a plane are $(331),$ calculate the planar density of atoms.