Proof That Any Vector Can Be Written In Terms Of Reciprocal Vectors


Given sets of reciprocal vectorsandthen any vectorcan be written in terms of


Use the identityand rearrange it to givevec u cdot (vec v times vec w ) =vec w cdot (vec u times vec v )= vec v cdot (vec u times vec v ) hence(1)

From the definitions of vec a' , vec b' , vec c',we can write (1) as