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Find u x v, v x u, and v x v. u = (-6, 2, -7) v = (-2, -5, -3) (a) u x V 29i+ 4j + 26k (b) V x u −29i — 4j – 26k X X

Find u x v, v x u, and v x v. u = (-6, 2, -7) v = (-2, -5, -3) (a) u x V 29i+ 4j + 26k (b) V x u −29i — 4j – 26k X X

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Cross Product and Dot Product Problems** Given vectors **u** and **v**: \[ \mathbf{u} = \langle -6, 2, -7 \rangle \] \[ \mathbf{v} = \langle -2, -5, -3 \rangle \] Find \( \mathbf{u} \times \mathbf{v} \), \( \mathbf{v} \times \mathbf{u} \), and \( \mathbf{v} \cdot \mathbf{v} \). --- **(a) \( \mathbf{u} \times \mathbf{v} \)** Calculated Result: \[ 29\mathbf{i} + 4\mathbf{j} + 26\mathbf{k} \] (This result is incorrect.) --- **(b) \( \mathbf{v} \times \mathbf{u} \)** Calculated Result: \[ -29\mathbf{i} - 4\mathbf{j} - 26\mathbf{k} \] (This result is incorrect.) --- **(c) \( \mathbf{v} \cdot \mathbf{v} \)** Calculated Result: \[ 0 \] (This result is correct.) --- **Explanation:** - **Cross Product:** The cross product \(\mathbf{u} \times \mathbf{v}\) should yield a vector perpendicular to both **u** and **v**. - **Order:** \(\mathbf{v} \times \mathbf{u} = -(\mathbf{u} \times \mathbf{v})\). - **Dot Product:** \(\mathbf{v} \cdot \mathbf{v}\) results in a scalar representing the squared magnitude of vector **v**. Please verify your calculations for \( \mathbf{u} \times \mathbf{v} \) and \( \mathbf{v} \times \mathbf{u} \).
Transcribed Image Text:**Cross Product and Dot Product Problems** Given vectors **u** and **v**: \[ \mathbf{u} = \langle -6, 2, -7 \rangle \] \[ \mathbf{v} = \langle -2, -5, -3 \rangle \] Find \( \mathbf{u} \times \mathbf{v} \), \( \mathbf{v} \times \mathbf{u} \), and \( \mathbf{v} \cdot \mathbf{v} \). --- **(a) \( \mathbf{u} \times \mathbf{v} \)** Calculated Result: \[ 29\mathbf{i} + 4\mathbf{j} + 26\mathbf{k} \] (This result is incorrect.) --- **(b) \( \mathbf{v} \times \mathbf{u} \)** Calculated Result: \[ -29\mathbf{i} - 4\mathbf{j} - 26\mathbf{k} \] (This result is incorrect.) --- **(c) \( \mathbf{v} \cdot \mathbf{v} \)** Calculated Result: \[ 0 \] (This result is correct.) --- **Explanation:** - **Cross Product:** The cross product \(\mathbf{u} \times \mathbf{v}\) should yield a vector perpendicular to both **u** and **v**. - **Order:** \(\mathbf{v} \times \mathbf{u} = -(\mathbf{u} \times \mathbf{v})\). - **Dot Product:** \(\mathbf{v} \cdot \mathbf{v}\) results in a scalar representing the squared magnitude of vector **v**. Please verify your calculations for \( \mathbf{u} \times \mathbf{v} \) and \( \mathbf{v} \times \mathbf{u} \).
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