Thread: Coordinate systems, crystallography, Basis of Vector Space question

The vectors v1=[2.6; -1.5; 0]
v2=[0, 3, 0]
v3=[0, 0, 4.8]
form a basis for unit cell for a crystal lattice of titanium. (units in Angstroms) I know that in alloys of titanium, some additional atoms may be in the unit cell at the octahedral and tetrahedral sites (so named this because of the geometric objects formed by atoms at these locations. One of the octahedral sites is [1/2; 1/4; 1/6] relative to the lattice basis. Determine the coordinates of this site relative to the standard basis of R3(3-space). What should I do?

Off-hand, I'd say you're to perform this calculation: (1/2) v1 + (1/4) v2 + (1/6) v3, since the lattice basis is expressed in terms of the standard basis.