If `vecx.veca=0vecx.vecb=0 and vecx.vecc=0` for some non zero vector `vecx` then show that `[veca vecb vecc]=0`

If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr , then the value of [(veca, vecb, vecc)] is

If vecr.veca=0,vecr.vecb=0andvecr.vecc=0 for some non-zero vector vecr , then the value of veca.(vecbxxvecc) is…… .

If vecX.vecA=0, vecX.vecB=0,vecX.vecC=0 for some non-zero vector, vecX , then [vecAvecBvecC]=0

Let vecr be a non - zero vector satisfying vecr.veca = vecr.vecb =vecr.vecc =0 for given non- zero vectors veca vecb and vecc Statement 1: [ veca - vecb vecb - vecc vecc- veca] =0 Statement 2: [veca vecb vecc] =0

If vecr.veca=vecr.vecb=vecr.vecc=1/2 for some non zero vector vecr and veca,vecb,vecc are non coplanar, then the area of the triangle whose vertices are A(veca),B(vecb) and C(vecc0 is (A) |[veca vecb vecc]| (B) |vecr| (C) |[veca vecb vecr]vecr| (D) none of these

given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=vecc .

given that veca. vecb = veca.vecc, veca xx vecb= veca xx vecc and veca is not a zero vector. Show that vecb=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 and vecc are three non - zero and non - coplanar vectors such that [(veca,vecb,vecc)]=4 , then the value of (veca+3vecb-vecc).((veca-vecb)xx(veca-2vecb-3vecc)) equal to