Prove that `veca,vecb,vecc` are coplanar iff `vecaxxvecb,vecbxxvecc,veccxxveca` are coplanar

If veca,vecb,vecc are coplanar, show that veca+vecb, vecb+vecc, vecc+veca are also coplanar.

If veca,vecb,vecc are coplanar then show that vecaxxvecb, vecbxxvecc and veccxxveca are also coplanar.

Prove that [vecaxxvecb, vecbxxvecc, veccxxveca] = [[veca.veca, veca.vecb, veca.vecc], [veca.vecb,vecb.vecb, vecb.vecc], [veca.vecc, vecb.vecc,vecc.vecc]] = [veca, vecb, vecc]^2,Hence show that vectors vecaxxvecb, vecbxxvecc, veccxxveca are non-coplanar if and only if vectors veca, vecb, vecc are non-coplanar

If veca+vecb+vecc=0 , prove that (vecaxxvecb)=(vecbxxvecc)=(veccxxveca)

If veca, vecb, vecc are three vectors, then [(vecaxxvecb, vecbxxvecc, veccxxveca)]=

If the three vectors veca,vecb,vecc are non coplanar express each of vecbxxvecc, veccxxveca, vecaxxvecb in terms of veca,vecb,vecc .

If veca,vecb,vecc and vecd are unit vectors such that (vecaxxvecb).(veccxxvecd)=1 and veca.vecc=1/2 then (A) veca,vecb,vecc are non coplanar (B) vecb,vecc, vecd are non coplanar (C) vecb, vecd are non paralel (D) veca, vecd are paralel and vecb, vecc are parallel

Show that the vectors 2veca-vecb+3vecc, veca+vecb-2vecc and veca+vecb-3vecc are non-coplanar vectors (where veca, vecb, vecc are non-coplanar vectors).

If vector veca,vecb,vecc are coplanar show that |(veca,vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|

If veca, vecb, vecc are non coplanar non null vectors such that [(veca, vecb, vecc)]=2 then {[(vecaxxvecb, vecbxxvecc, veccxxveca)]}^(2)=