Determine the hexagonal close?packed lattice directions of the lines rt, ut, and uv in the figure for this problem. To do this, first determine the vector projection of a line in the basal plane and then add it to the c axis projection of the line. Note that the direction indices of the c axis are [0001], and that if [0001] is considered a vector its magnitude will equal the height    of the unit cell.    A unit distance along a diagonal axis of Type I, such as the distance or, equals one third of the length of [2110] in Fig. 1.20. The magnitude of this unit is thus equal to 1/3 [2110]. Combine these two quantities to obtain the direction indices of each of the lines.


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