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Exercise 2.7.17

Avg difficulty 3.0

Use the formula from Exercise 47 to show that

(u×v)⋅((v×w)×(w×z))=((v×w)⋅z) ((u×v)⋅w).(\mathbf{u}\times\mathbf{v})\boldsymbol{\cdot}((\mathbf{v}\times\mathbf{w})\times(\mathbf{w}\times\mathbf{z}))=((\mathbf{v}\times\mathbf{w})\boldsymbol{\cdot}\mathbf{z})\,((\mathbf{u}\times\mathbf{v})\boldsymbol{\cdot}\mathbf{w}).

Selinger, Matrix Theory and Linear Algebra, Vectors in Rn, The cross product, Exercise 2.7.17

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Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.