`veca,vecb` and `vecc` are three non-coplanar vectors and r is any arbitrary vector. Prove that `[[vecb, vecc,vec r]]veca + [[vecc, veca, vecr]]vecb +[[veca,vec b,vec r]]vecc = [[veca,vec b, vecc]]vecr`

veca , vecb and vecc are three non-coplanar vectors and vecr . Is any arbitrary vector. Prove that [vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr .

Statement 1: Any vector in space can be uniquely written as the linear combination of three non-coplanar vectors. Stetement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then [(veca,vecb, vecc)]vecc+[(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb=[(veca, vecb, vecc)]vecr

If veca, vecb, vecc are three non-zero non-null vectors are vecr is any vector in space then [(vecb, vecc, vecr)]veca+[(vecc, veca, vecr)]vecb+[(veca, vecb, vecr)]vecc is equal to

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

If veca,vecb and vecc are non coplnar and non zero vectors and vecr is any vector in space then [vecc vecr vecb]veca+pveca vecr vecc] vecb+[vecb vecr veca]c= (A) [veca vecb vecc] (B) [veca vecb vecc]vecr (C) vecr/([veca vecb vecc]) (D) vecr.(veca+vecb+vecc)

Statement 1: Let vecr be any vector in space. Then, vecr=(vecr.hati)hati+(vecr.hatj)hatj+(vecr.hatk)hatk Statement 2: If veca, vecb, vecc are three non-coplanar vectors and vecr is any vector in space then vecr={([(vecr, vecb, vecc)])/([(veca, vecb, vecc)])}veca+{([(vecr, vecc, veca)])/([(veca, vecb, vecc)])}vecb+{([(vecr, veca, vecb)])/([(veca, vecb, vecc)])}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

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

If veca, vecb, vecc are three non-coplanar vectors, then a vector vecr satisfying vecr.veca=vecr.vecb=vecr.vecc=1 , is

If veca, vecb and vecc 1 are three non-coplanar vectors, then (veca + vecb + vecc). [(veca + vecb) xx (veca + vecc)] equals