primitive vectors and primitive cell volume for a bcc lattice.

Dear student,
A Bravais lattice is defined as an infinite array of discrete points generated by a set of discrete translation vectors given by:

Here n_i are integers and a_i are known as the primitive vectors which lie in different directions and span the lattice completely. These discrete set of vectors must be closed under vector addition and subtraction. Hence, for any choice of position vector R, the lattice looks exactly the same.
The volume of the unit cell spanned by the discrete translation vectors is known as the Primitive cell volume.
Regards
Sumit