Answered: Let u, v, and w be three mutually…

Let u, v, and w be three mutually perpendicular vectors in ℝ3.(a) Prove that u × (v × w) = 0.(b) Show that |u · (v × w)|= ||u || ||v|| ||w|| .

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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Question

Let u, v, and w be three mutually perpendicular vectors in ℝ³.
(a) Prove that u × (v × w) = 0.
(b) Show that |u · (v × w)|= ||u || ||v|| ||w|| .

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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