Question $3$

$($a$)$ Determine the Miller indices for the directions A and B in Figure $1,$ showing how you

arrived at your answers by first beginning with the coordinates. How long is Vector A $,$

in terms of the lattice parameter $a.$

$(10$ marks$)$

$($b$)$ Determine the Miller indices for the planes shown in Figures $2$ and $3.$ Show how you

arrived at your answers by first beginning with the intercepts. State or indicate the

corner where the intercepts are measured from. What is the interplanar distance of the

plane in Figure $2$ in terms of the lattice parameter $a?$

$(10$ marks$)$

Figure ${?}^{**}$