Hi please show that it satisfies it. Thank you! Show all work and explanation please. The scalar product of two vectors Ã and B in terms of their components is Ã. B = A„Bµ+A„By+A̟B¿. The components of the vector product of these vectors in terms of their components are(Ах В). — А, В, - А, Ву,(Ах В), — А,В.— А,В-,(Ã× B); = A,By - A,Bz.%3DShow thatĀ · (B x T) = B · (Č x Ã) = · (Ã × B),Ä × (B x C) = B(Ã· Č) – Č(Ã · B).Hint: In the second equation, take the x-component of both sides of the equation. It is sufficient toprove it only for the x-component because all components should satisfy the same vector identity.

Let, vector A→=Axi^+Ayj^+Azk^, B→=Bxi^+Byj^+Bzk^,…

Answered: Show that Ä: (B x C) = B · (C × Ã) = Ĉ…

Science

Physics

Show that Ä: (B x C) = B · (C × Ã) = Ĉ · (Ä × B), Ã × (B x C) = B(Ä… Č) – Č(Ä · B). %3D

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.11P

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Question

Hi please show that it satisfies it. Thank you! Show all work and explanation please.

The scalar product of two vectors Ã and B in terms of their components is Ã. B = A„Bµ+A„By+
A̟B¿. The components of the vector product of these vectors in terms of their components are
(Ах В). — А, В, - А, Ву,
(Ах В), — А,В.— А,В-,
(Ã× B); = A,By - A,Bz.
%3D
Show that
Ā · (B x T) = B · (Č x Ã) = · (Ã × B),
Ä × (B x C) = B(Ã· Č) – Č(Ã · B).
Hint: In the second equation, take the x-component of both sides of the equation. It is sufficient to
prove it only for the x-component because all components should satisfy the same vector identity.

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