Show that `vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=vec0.`

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

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

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 the vectors veca, vecb, and vecc are coplanar show that |(veca,vecb,vecc),(veca.veca, veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc)|=0

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

Prove that [veca-vecb,vecb-vecc,vecc-veca]=0

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.

If veca =2veci+3vecj-veck , vecb =2veci+5veck , vecc =vecj-3veck , verify that vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc .

If veca,vecb, vecc and veca',vecb',vecc' are reciprocal system of vectors, then prove that veca'xxvecb'+vecb'xxvecc'+vecc'xxveca'=(veca+vecb+vecc)/([vecavecbvecc])

If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively of a triangle ABC then (A) veca.(vecbxxvecc)=vec0 (B) vecaxx(vecbxvecc)=vec0 (C) veca.vecb=vecc=vecc=veca.a!=0 (D) vecaxxvecb+vecbxxvecc+veccxxvecavec0