Property 5: Vectors `veca, vecb` and `vecc` are non-coplanar iff vectors `veca' , vecb'` and `vecc'` are non-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 and vecC are coplanar vectors, then

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).

Given three vectors veca, vecb and vecc are non-zero and non-coplanar vectors. Then which of the following are coplanar.

If veca,vecb,vecc be three non coplanar vectors show that vecbxxvecc,veccxxveca,vecaxxvecb are non coplanar.

Show that the vectors veca-2vecb+3vecc,-2veca+3vecb-4vecc and - vecb+2vecc are coplanar vector where veca, vecb, vecc are non coplanar vectors

If (vecaxxvecb)xx(vecbxxvecc)=vecb, where veca,vecb and vecc are non zero vectors then (A) veca,vecb and vecc can be coplanar (B) veca,vecb and vecc must be coplanar (C) veca,vecb and vecc cannot be coplanar (D) none of these

If non-zero vectors veca and vecb are equally inclined to coplanar vector vecc , then vecc can be

If veca, vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,7vecb-9vecc,10vecc-23veca)]

If vector veca,vecb,vecc are coplanar then find the value of vecc in terms of veca and vecb