fron Naive Lie theory (John Stillwell)Need help with attached highligted 1.4.4Thankyou ExercisesThe cross product is an operation on Ri+Rj+Rk because u x v is in Ri+Rj+Rkfor any u, v E Ri+Rj+Rk. However, it is neither a commutative nor associativeoperation, as Exercises 1.4.1 and 1.4.3 show.1.4.1 Prove the antisymmetric property u × v = –v × u.1.4.2 Prove that u × (v × w) = v(u ·w) – w(u ·v) for pure imaginary u, v, w.1.4.3 Deduce from Exercise 1.4.2 that x is not associative.1.4.4 Also deduce the Jacobi identity for the cross product:их (vx w)+wx (ихv) +vx (wxх и) — 0.The antisymmetric and Jacobi properties show that the cross product is not com-pletely lawless. These properties define what we later call a Lie algebra.

Introduction: We know that u×v×w=vu·w-wu·v, where u, v, and w are purely imaginary.

Answered: Also deduce the Jacobi identity for the…

Advanced Engineering Mathematics

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Also deduce the Jacobi identity for the cross product: u × (v × w) +w × (u × v) +v × (w x u) = 0 их