If `veca,vecb and vecc` are non coplnar and non zero vectors and `vecr` is any vector in space then`[vecc vecr vecb]veca+[veca 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)`

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecxxvecb),(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)= (A) [veca vecb vecc] (B) 2[veca vecb vecc]vecr (C) 3[veca vecb vecc]vecr (D) 4[veca vecb vecc]vecr

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecxxvecb),(vecrxxvecc)+(vecb xxvecc)xx(vecrxxveca)+(veccxxveca)xx(vecrxxvecb)= (A) [veca vecb vecc] (B) 2[veca vecb vecc]vecr (C) 3[veca vecb vecc]vecr (D) 4[veca vecb 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 .

[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb vecc ] , then

vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors and vec r is any vector in space, then ( veca × vecb )×( vecr × vecc )+( vecb × vecc )×( vecr × veca )+( vecc × veca )×( vecr × vecb ) is equal to

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

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=(vecbxxvecc)/([vecb vecc veca]), vecB=(veccxxveca)/([vecc veca vecb]), vecC=(vecaxxvecb)/([veca vecb vecc]) find [vecA vecB vecC]

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

If veca,vecb and vecc are non coplaner vectors such that vecbxxvecc=veca , veccxxveca=vecb and vecaxxvecb=vecc then |veca+vecb+vecc| =