Find u x v. u = j + 3k, v = 7i - k Show that u x v is orthogonal to both u and v. (u x v) · u = (u x v) · v =
Find u x v. u = j + 3k, v = 7i - k Show that u x v is orthogonal to both u and v. (u x v) · u = (u x v) · v =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Topic: Cross Product and Orthogonality**
**Objective**: Calculate the cross product of two vectors and demonstrate orthogonality.
---
**Problem Statement**:
**Find** \( \mathbf{u} \times \mathbf{v} \).
Given vectors:
\[ \mathbf{u} = \mathbf{j} + 3\mathbf{k} \]
\[ \mathbf{v} = 7\mathbf{i} - \mathbf{k} \]
\[ \text{Cross Product:} \]
\[ \boxed{\phantom{answer}} \]
---
**Show that** \( \mathbf{u} \times \mathbf{v} \) **is orthogonal to both** \( \mathbf{u} \) **and** \( \mathbf{v} \).
**Dot Product Verification**:
\[ (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{u} = \boxed{\phantom{answer}} \]
\[ (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{v} = \boxed{\phantom{answer}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcffe6fb8-a8b1-4738-951c-b41ccaeecf4e%2Fa018d844-974b-4408-a2e1-4ee1ae1116f9%2F3wdys5_processed.png&w=3840&q=75)
Transcribed Image Text:**Topic: Cross Product and Orthogonality**
**Objective**: Calculate the cross product of two vectors and demonstrate orthogonality.
---
**Problem Statement**:
**Find** \( \mathbf{u} \times \mathbf{v} \).
Given vectors:
\[ \mathbf{u} = \mathbf{j} + 3\mathbf{k} \]
\[ \mathbf{v} = 7\mathbf{i} - \mathbf{k} \]
\[ \text{Cross Product:} \]
\[ \boxed{\phantom{answer}} \]
---
**Show that** \( \mathbf{u} \times \mathbf{v} \) **is orthogonal to both** \( \mathbf{u} \) **and** \( \mathbf{v} \).
**Dot Product Verification**:
\[ (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{u} = \boxed{\phantom{answer}} \]
\[ (\mathbf{u} \times \mathbf{v}) \cdot \mathbf{v} = \boxed{\phantom{answer}} \]
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