Problem $2$: Draw the $[2113]$ direction in the HCP unit cell below.

Algorithm for Miller$-$Bravais Coordinates in HCP:

Remove brackets.

Divide by largest integer so all values are $1.$

Multiply terms by appropriate unit cell dimension a

$($for a$1,$ a$2,$ and a$3$ axes$)$ or c $($for z $-$axis$)$ to produce

projections.

Construct vector by placing tail at origin and stepping

off these projections to locate the head.

Problem $2$: Draw the $[$II$23]$ direction in the HCP unit cell below.