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Find u x v. u = (1, -2, 0), v = (1, 0, -1) Show that ux vis orthogonal to both u and v. (u x V) u = (u x V). V =

Find u x v. u = (1, -2, 0), v = (1, 0, -1) Show that ux vis orthogonal to both u and v. (u x V) u = (u x V). V =

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Cross Product and Orthogonality** **Problem 1: Find \( \mathbf{u} \times \mathbf{v} \).** - Given vectors: - \( \mathbf{u} = (1, -2, 0) \) - \( \mathbf{v} = (1, 0, -1) \) [Box for answer] **Problem 2: Show that \( \mathbf{u} \times \mathbf{v} \) is orthogonal to both \( \mathbf{u} \) and \( \mathbf{v} \).** - Calculate the dot product: - \( (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{u} = \) [Box for answer] - \( (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{v} = \) [Box for answer]
Transcribed Image Text:**Cross Product and Orthogonality** **Problem 1: Find \( \mathbf{u} \times \mathbf{v} \).** - Given vectors: - \( \mathbf{u} = (1, -2, 0) \) - \( \mathbf{v} = (1, 0, -1) \) [Box for answer] **Problem 2: Show that \( \mathbf{u} \times \mathbf{v} \) is orthogonal to both \( \mathbf{u} \) and \( \mathbf{v} \).** - Calculate the dot product: - \( (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{u} = \) [Box for answer] - \( (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{v} = \) [Box for answer]
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