In Physics and solid Chemistry we come across various lattice structures ... In this applet you will see that how to form a reciprocal system of a basis system of 3 vectors in R^3 space ...[br][br]consider that a,b,c are the three non coplanar non zero vectors in R^3,[br]if we construct a system of a',b',c' such that [br]a.a'=b.b'=c.c'=1 [br]then a',b',c' is the reciprocal system of basis a,b,c ...[br][br]we can find them by using the Scalar Triple Product...[br]as[br] a.(b x c) = b.(c x a)=c.(a x b)=[a b c] ,[br]=> a.((b x c)/[a b c]) = b.((c x a)/[a b c]) = c.((a x b)/[a b c]) = 1[br][br](as [a b c] is scalar..)[br][br]hence a'=(b x c)/[a b c] , b'=(c x a)/[a b c] , c'=(a x b)/[a b c][br]observe that a' is perpendicular to plane of b and c ,[br]b' is perpendicular to plane of c and a , and hence so c'.