Consider three arbitrary vectors u, v, w E R³. Using the definitions of the cross and dot products, prove that the scalar triple product is invariant under circular permutations of the operands, i.e. that: u (vxw)=w (uxv) = v. (wxu)

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.1: Length And Dot Product In R^n
Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...
icon
Related questions
Question
Consider three arbitrary vectors u, v, w E R³. Using the definitions of the cross and
dot products, prove that the scalar triple product is invariant under circular
permutations of the operands, i.e. that:
u (vxw)=w (uxv) = v. (wxu)
Transcribed Image Text:Consider three arbitrary vectors u, v, w E R³. Using the definitions of the cross and dot products, prove that the scalar triple product is invariant under circular permutations of the operands, i.e. that: u (vxw)=w (uxv) = v. (wxu)
Expert Solution
steps

Step by step

Solved in 5 steps

Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage