Show that `(veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vecd) +(vecc xx veca) *(vecb xx vecd)=0`.

If veca,vecb,vecc,vecd be vectors such that [vecavecbvecc]=2 and (vecaxxvecb) xx (vecc xx vecd)+(vecb xx vecc) xx (veca xx vecd) + (vecc xx veca) xx (vecb xx vecd)=-muvecd Then the value of mu is

If vectors, vecb, vcec and vecd are not coplanar, the pove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

Let veca, vecb and vecc are three unit vectors in a plane such that they are equally inclined to each other, then the value of (veca xx vecb).(vecb xx vecc) + (vecb xx vecc). (vecc xx veca)+(vecc xx veca). (veca xx vecb) can be

Prove that: (vecaxxvecb)xx(veccxxvecd)+(vecaxxvecc)xx(vecd xx vecb)+(vecaxxvecd)xx(vecbxxvecc)=-2[vecb vecc vecd] veca

[(veca xxvecb)xx(vecb xx vecc) (vecb xxvecc) xx (vecc xxveca) (veccxxveca) xx (veca xx vecb)] is equal to ( where veca, vecb and vecc are non - zero non- colanar vectors).

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

If veca, vecb,vecc and vecd are distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

[vecaxx vecb " " vecc xx vecd " " vecexx vecf] 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

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