Prove that:` (2veca-vecb)xx``(veca+2vecb)=5vecaxxvecb`.

Prove that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb) also interpret this result.

Prove that: |(veca+vecb)xx(veca-vecb)|=2ab if veca_|_vecb

Prove that (veca+3vecb)xx(veca+vecb)+(3veca-5vecb)xx(veca-vecb)=0

Prove that: [(vecaxxvecb)xx(vecaxxvecc)].vecd=[veca vecb vecc](veca.vecd)

Prove that (veca+ vecb)*( veca+ vecb)=|veca|^2+| vecb|^2 , if and only if veca , vecb are perpendicular, given veca!= vec0, vecb!= vec0

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

Prove that : veca*(vecb+vec c)xx(veca+2vecb+3vec c)=[veca vecb vec c]

Prove that (vecaxxvecb)^(2)= |(veca.veca" "veca.vecb),(veca.vecb" "vecb.vecb)|

Prove that veca*(vecb+vec c)xx (veca+3vecb+2vec c)=-(veca vecb vecc )

Let veca,vecb and vecc be a set of non- coplanar vectors and veca'vecb' and vecc' be its reciprocal set. prove that veca=(vecb'xxvecc')/([veca'vecb'vecc']),vecb=(vecc'xxveca')/([veca'vecb'vecc'])andvecc=(veca'xxvecb')/([veca'vecb'vecc'])