Classical Dynamics of Particles and Systems · Problem 1-24

Newtonian Mechanics—Single Particle — Marion & Thornton

Physics — Mechanics · vector-decomposition

Problem

Let A\mathbf{A} be an arbitrary vector, and let e\mathbf{e} be a unit vector in some fixed direction. Show that A=e(A⋅e)+e×(A×e)\mathbf{A} = \mathbf{e}(\mathbf{A} \cdot \mathbf{e}) + \mathbf{e} \times (\mathbf{A} \times \mathbf{e}) What is the geometrical significance of each of the two terms of the expansion?

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