Prove that `veca\'.(vecb+vecc)+vecb\'.(vecc+veca)+vecc\'.(veca+vecb)=0`

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

If veca, vecb, vecc are non-null non coplanar vectors, then [(veca-2vecb+vecc, vecb-2vecc+veca, vecc-2veca+vecb)]=

Prove that [ veca+ vecb , vecb+ vecc , vecc+ veca]=2[ veca , vecb , vecc] .

If veca, vecb, vecc are non-coplanar vectors, then (veca.(vecb xx vecc))/(vecb.(vecc xx veca)) + (vecb.(vecc xx veca))/(vecc.(veca xx vecb)) +(vecc.(vecb xx veca))/(veca. (vecb xx vecc)) is equal to:

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

Let veca , vecb,vecc be three vectors such that veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 , |vecc| =3 , " then " | veca + vecb + vecc| is,

Prove that [veca+vecb,vecb+vecc,vecc+veca]=2[veca vecb vecc]

Prove that veca. [(vecb + vecc) xx (veca + 3 vecb + 4 vecc) ]= [{:(veca,vecb,vecc):}]

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'vecb' and vecc' be its reciprocal set. prove that veca=(vecb'xxvecc')/([veca'vecb'vecc']),vecb=(vecc'xxveca')/([veca'vecb'vecc'])andvecc=(veca'xxvecb')/([veca'vecb'vecc'])