Prove that `(vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc`

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

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

Prove that: [vecaxxvecb vecb xx vecc veccxxveca]=[vecavecbvecc]^2

If vecP = (vecbxxvecc)/([vecavecbvecc]).vecq=(veccxxveca)/([veca vecb vecc])and vecr = (vecaxxvecb)/([veca vecbvecc]), " where " veca,vecb and vecc are three non- coplanar vectors then the value of the expression (veca + vecb + vecc ). (vecq+ vecq+vecr) is

Let veca,vecb, vecc be any three vectors, Statement 1: [(veca+vecb, vecb+vecc,vecc+veca)]=2[(veca, vecb, vecc)] Statement 2: [(vecaxxvecb, vecbxxvecc, veccxxveca)]=[(veca, vecb, vecc)]^(2)

If vecr=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca) and [veca vecb vecc]=(1)/(3) , then x+y+z is equal to

If vec(alpha)=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca) and [veca vecb vecc]=1/8 , then x+y+z=

For any four vectors, prove that ( veca × vecb )×( vecc × vecd )=[ veca vecc vecd ] vecb −[ vecb vecc vecd ] veca

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'])

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