## The Relationship Between Sets of Reciprocal Vectors

Theorem

Ifandare sets of reciprocal vectors, and(1) then

Proof

Sinceandare perpendicular sets,

Substitute (1) into these expressions, obtaining

Then

Now use the identityhence

Theorem

Ifandare sets of reciprocal vectors, and(1) then

Proof

Sinceandare perpendicular sets,

Substitute (1) into these expressions, obtaining

Then

Now use the identityhence