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

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

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

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

For any four vectors, prove that ( veca × vecb )×( vecc × vecd )=[ veca vecc vecd ] vecb −[ vecb vecc vecd ] veca

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

The value of veca.(vecb+vecc)xx(veca+vecb+vecc) , is

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

For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc = |veca||vecb||vecc| holds if and only if

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

Let veca , vecb,vecc be three vectors such that veca bot ( vecb + vecc), vecb bot ( vecc + veca) and vecc bot ( veca + vecb) , " if " |veca| =1 , |vecb| =2 , |vecc| =3 , " then " | veca + vecb + vecc| is,