Prove that `vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=0`

For three non - zero vectors veca, vecb and vecc , if [(veca, vecb , vecc)]=4 , then [(vecaxx(vecb+2vecc), vecbxx(vecc-3veca), vecc xx(3veca+vecb))] is equal to

Prove that veca\'.(vecb+vecc)+vecb\'.(vecc+veca)+vecc\'.(veca+vecb)=0

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|

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|

For any three vectors veca, vecb, vecc the value of vecaxx(vecbxxvecc)+vecbxx(veccxxveca)+veccxx(vecaxxvecb) , is

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

Prove that vecaxx{vecbxx(veccxxvecd)}=(vecb.vecd)(vecaxxvecc)-(vecb.vecc)(vecaxxvecd)

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

Prove that: vecaxx[vecbxx(veccxxveca)]=(veca.vecb)(vecaxxvecc)