Proof of Conditions For Sets of Vectors To Be Reciprocal
Two sets of vectorsandare said to be reciprocal if and only if
Sets of vectorsandare reciprocal ifand (1)
From the last equation we concude thatis orthogonal toandso is in the same direction asand we can write
Taking the dot product of this on the left bygives
The same argument givesand
Alsoand similarly forand
Finally,sinceis perpendicular toand similarly for all the dot products in (1).