If `veca,vecb,vecc and vecas\', vecb\', vecc\'` are reciprocal system of vectors prove that `vecaxxvecb+vecbxxvecb+veccxxvecc\'=vec0`

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])

If veca, vecb, vecc and veca', vecb', vecc' form a reciprocal system of vectors then [(veca', vecb', vecc')]=

If veca, vecb, vecc and veca', vecb', vecc' form a reciprocal system of vectors then veca.veca'+vecb.vecb'+vecc.vecc'=

Let veca, vecb , vecc be non -coplanar vectors and let equations veca', vecb', vecc' are reciprocal system of vector veca, vecb ,vecc then prove that veca xx veca' + vecb xx vecb' + vecc xx vecc' is a null vector.

Let veca, vecb , vecc be non -coplanar vectors and let equations veca', vecb', vecc' are reciprocal system of vector veca, vecb ,vecc then prove that veca xx veca' + vecb xx vecb' + vecc xx vecc' is a null vector.

Let veca, vecb and vec c be any three vectors; then prove that [[vecaxxvecb, vecbxxvecc, veccxxveca]] = [[veca, vecb, vecc]]^2

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 veca.vecb\'=veca.veca\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . [veca,vecb,vecc]-(veca\'xxvecb\')+(vecb\'xxvec\')+(vecc\'xxveca\')= (A) veca+vecb+vecc (B) veca+vecb-vecc (C) 2(veca+vecb+vecc) (D) 3(veca\'+vecb\'+vecc\')

If veca, vecb and vecc be three non-coplanar vectors and a',b' and c' constitute the reciprocal system of vectors, then prove that i. vecr=(vecr.veca')veca+(vecr.vecb')vecb+(vecr.vecc')vecc ii. vecr= (vecr.veca)veca'+(vecr.vecb)vecb' + (vecr.vecc) vecc'

If veca, vecb and vecc be three non-coplanar vectors and a',b' and c' constitute the reciprocal system of vectors, then prove that i. vecr=(vecr.veca')veca+(vecr.vecb')vecb+(vecr.vecc')vecc ii. vecr= (vecr.veca)veca'+(vecr.vecb)vecb' + (vecr.vecc) vecc'

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'veab' and vecc' be its reciprocal set. prove that veca=(b'xxc')/([veca'vecb'vecc']),vecb=(c'xxa')/([veca'vecb'vecc'])andvecc=(a'xxb')/([veca'vecb'vecc'])