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

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

Prove that veca. [(vecb + vecc) xx (veca + 3 vecb + 4 vecc) ]= [{:(veca,vecb,vecc):}]

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

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

If veca, vecb and vecc be any three non coplanar vectors. Then the system of vectors veca\',vecb\' and vecc\' which satisfies veca.veca\'=vecb.vecb\'=vecc.vecc\'=1 and veca.vecb\'=veca.vecc\'=vecb.veca\'=vecb.vecc\'=vecc.veca\'=vecc.vecb\'=0 is called the reciprocal system to the vectors veca,vecb, and vecc . The value of [veca\' vecb\' vecc\']^-1 is (A) 2[veca vecb vecc] (B) [veca vecb vecc] (C) 3[veca vecb vecc] (D) 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

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

[ veca + vecb vecb + vecc vecc + veca ]=[ veca vecb vecc ] , then

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

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|