If `veca.vecb=veca.vecc, vecaxxvecb=vecaxxvecc and veca!=vec0, ` then prove that `vecb=vecc.`

If veca, vecb and vecc are vectors such that veca. vecb = veca.vecc, veca xx vecb = veca xx vecc, a ne 0. then show that vecb = vecc.

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|

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|

veca,vecb,vecc are non zero vectors. If vecaxxvecb=vecaxxvecc and veca.vecb=veca.vecc then show that vecb=vecc .

If veca,vecb,vecc,vecd are four distinct vectors satisfying the conditions vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxecd then prove that veca.vecb+vecc.vecd!=veca.vecc+vecb.vecd

If vecax(vecaxxvecb)=vecbxx(vecbxxvecc) and veca.vecb!=0 , and [(veca,vecb,vecc)]=

If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vecd) is parallel to (vecb-vecc) . It is given that veca!=vecd and vecb!=vecc .

If veca, vecb, vecc are three given non-coplanar vectors and any arbitrary vector vecr in space, where Delta_(1)=|{:(vecr.veca,vecb.veca,vecc.veca),(vecr.vecb,vecb.vecb,vecc.vecb),(vecr.vecc,vecb.vecc,vecc.vecc):}|,Delta_(2)=|{:(veca.veca,vecr.veca,vecc.veca),(veca.vecb,vecr.vecb,vecc.vecb),(veca.vecc,vecr.vec ,vecc.vecc):}| Delta_(3)=|{:(veca.veca,vecb.veca,vecr.veca),(veca.vecb,vecb.vecb,vecr.vecb),(veca.vecc,vecb.vecc,vecr.vecc):}|'Delta=|{:(veca.veca,vecb.veca,vecc.veca),(veca.vecb,vecb.vecb,vecc.vecb),(veca.vecc,vecb.vecc,vecc.vecc):}|, "then prove that " vecr=(Delta_(1))/Deltaveca+(Delta_(2))/Deltavecb+(Delta_(3))/Deltavecc

Property 2 & 3: veca.vecb'=veca.vecc'=vecb.vecc'=vecc.veca'=0 and [[veca, vecb,vecc]][[veca',vecb',vecc']]=1

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