The figure above is a drawing of the reciprocal lattice crystal plane of fcc $(100).$

$$Suppose you are looking at FCC $(010)$ plane.

$($a$)$Draw FCC $(010)$ plane as shown in the figure above.

$($b$)$ Draw the interplanar distance of the real lattice & reciprocal space on the crystal plane $(010)$ you drew and write the miller index.

$($c$)$ If a$1=0\mathrm{.}1$nm$,$ a$2=0\mathrm{.}2$nm$,$ a$3=0\mathrm{.}4$nm$,$ find vector b$1,$ b$2,$ and distance on the reciprocal lattice $($a$).($Please include the units.$)$

$($d$)$ Find the interplanar distance that you arbitrarily set through the reciprocal lattice image.