Show that `(veca-vecb)xx(veca+vecb)=2(vecaxxvecb)`

Prove that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) .

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

If veca, vecb, vecc are vectors such that |vecb|=|vecc| then {(veca+vecb)xx(veca+vecc)}xx(vecbxxvecc).(vecb+vecc)=

If veca and vecb are two vectors, such that veca.vecbgt0 and |veca.vecb|=|vecaxxvecb| then the angle between the vectors veca and vecb is

If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ (vecb + veca) xx (2 veca + vecb)] = veca+vecb then angle theta " between " veca and vecb is

If vectors veca, vecb and vecc are coplanar, show that |{:(veca, vecb,vecc),(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc):}|=vec0

If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove that (vecbxx(veca xx vecb))/(vecb.vecb)=vecq

If veca,vecb and vecc are three non coplanar vectors and vecr is any vector in space, then (vecaxxvecb)xx(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 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