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If `veca,vecb, vecc and veca',vecb',vecc'` are reciprocal system of vectors, then prove that `veca'xxvecb'+vecb'xxvecc'+vecc'xxveca'=(veca+vecb+vecc)/([vecavecbvecc])`

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`veca'xxvecb'=((vecbxxvecc)xx(veccxxveca))/([vecavecbvecc]^(2))=({(vecbxxvecc).veca}vecc-{(vecbxxvecc).vecc}veca)/([vecavecbvecc]^(2))=([vecb vecc veca]vecc)/([vecabvecbvecc]^(2))=([veca vecb vecc]vecc)/([veca vecb vecc]^(2))=vecc/([veca vecb vecc])`
similarly, `vecb'xxvecc'=veca/([vecaxxvecbxxvecc])andvecc'xxveca' = vecb/([vecavecbvecc])`
Adding `veca'xxvecb'+vecb'xxvecc'+vecc'xxveca'=(veca+vecb+vecc)/([vecavecbvecc])`
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