please answer the following question.

Every periodic crystal structure has two lattices: real space lattice and reciprocal lattice. In the real space lattice, the crystal translation vector of a 3D lattice is dened as: T = 11.1611 + u2a2+u3a3, in which a1, a2, and as are basis vectors. Similarly, in the reciprocal lattice, the reciprocal lattice vector can be dened as: K = nlbl + n2b2+n3b3, in which b1, b2, and b3 are reciprocal basis vectors. The crystal translation vector T and the reciprocal lattice vector K satisfy the following condition: eiK'T = 1. Try derive this condition according to the translational symmetry of crystal, and also write the mathematical form (equation) of reciprocal basis vectors, b1, b2, and b3