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

If veca, vecba and vecc are non- coplanar vecotrs, then prove that |(veca.vecd)(vecbxxvecc)+(vecb.vecd)(veccxxveca)+(vecc.vecd)(vecaxxvecb) is independent of vecd where vecd is a unit vector.

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

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

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

If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd then (A) (veca-vecd)=lamda(vecb-vecc) (B) veca+vecd=lamda(vecb+vecc) (C) (veca-vecb)=lamda(vecc+vecd) (D) none of these

If veca,vecb,vecc and vecd are the position vectors of the vertices of a cycle quadrilateral ABCD, prove that (|vecaxxvecb+vecb xxvecd+vecd xxveca|)/((vecb-veca).(vecd-veca))+(|vecbxxvecc+veccxxvecd+vecd+vecd xx vecb|)/((vecb-vecc).(vecd-vecc))

If veca,vecb,vecc,vecd be vectors such that [vecavecbvecc]=2 and (vecaxxvecb) xx (vecc xx vecd)+(vecb xx vecc) xx (vecc xx vecd) + (vecc xx veca) xx (vecb xx vecd)=-muvecd Then the value of mu 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 vectors, vecb, vecc and vecd are not coplanar, the prove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

A, B C and D are four points in a plane with position vectors, veca, vecb vecc and vecd respectively, such that (veca-vecd).(vecb-vecc)= (vecb-vecd).(vecc-veca)=0 then point D is the ______ of triangle ABC.