Show that: `(veca+vecb).{(vecb+vecc)xx(vecc+veca)|=2{veca.(vecbxxvecc)}`

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

If veca,vecb,vecc are linearly independent vectors, then ((veca+2vecb)xx(2vecb+vecc).(5vecc+veca))/(veca.(vecbxxvecc)) is equal to

Show that: (veca-vecd)xx(vecb-vecc)+(vecb-vecd)xx(vecc-veca)+(vecc-vecd)xx(veca-vecb) is independent of vecd .

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Prove that (vecbxxvecc)xx(veccxxveca)=[veca vecb vecc]vecc

Let veca,vecb, vecc be any three vectors, Statement 1: [(veca+vecb, vecb+vecc,vecc+veca)]=2[(veca, vecb, vecc)] Statement 2: [(vecaxxvecb, vecbxxvecc, veccxxveca)]=[(veca, vecb, vecc)]^(2)

If vecb and vecc are any two orthogonal unit vectors and veca is any vector, then (veca.vecb)vecb + (veca.vecc)vecc + (veca.(vecb xx vecc))/|vecb xx vecc|^(2) (vecb xx vecc) =

Show that [veca vecb vecc]\^2=|(veca.veca,veca.vecb,veca.vecc),(vecb.veca,vecb.vecb,vecb.vecc),(vecc.veca,vecc.vecb,vecc.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

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