a$.$ In a hexagonal lattice what are the indices of the $[11-22]$ vector in $3-$index notation? Find the

length of $[11-22]$ in Mg$,$ which is a hexagonal close$-$packed metal, with a unit cell a$=3\mathrm{.}21,$ c

$=5\mathrm{.}21.$

b$.$ Draw the $(0001)$ basal plane and show that the vector described in the $4-$ and $3$ index notation

leads to the same endpoint in the projection onto this plane. Note that you have to use several unit cells. This is also a test of your answer in a$.$