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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Question
![**Problem Statement:**
Find the length and direction (when defined) of **u × v** and **v × u**.
Given vectors:
\[ \mathbf{u} = 2\mathbf{i} - 2\mathbf{j} - \mathbf{k} \]
\[ \mathbf{v} = \mathbf{i} - \mathbf{k} \]
**Explanation:**
- **Vector u** is represented as \(2\mathbf{i} - 2\mathbf{j} - \mathbf{k}\).
- Here, \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are the unit vectors along the x, y, and z axes respectively.
- **Vector v** is represented as \(\mathbf{i} - \mathbf{k}\).
**Objective:**
1. Calculate the cross product **u × v**.
2. Calculate the cross product **v × u**.
3. Determine the length (magnitude) of each cross product.
4. Identify the direction for each vector cross product using the right-hand rule.
**Note:** The cross product of two vectors results in a vector that is perpendicular to the plane formed by the original vectors.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff59b6538-146c-4e69-9177-ffcf13d9c3a9%2Fe39827aa-70be-40fd-aa8e-568bded55d17%2Ftli3ng9_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the length and direction (when defined) of **u × v** and **v × u**.
Given vectors:
\[ \mathbf{u} = 2\mathbf{i} - 2\mathbf{j} - \mathbf{k} \]
\[ \mathbf{v} = \mathbf{i} - \mathbf{k} \]
**Explanation:**
- **Vector u** is represented as \(2\mathbf{i} - 2\mathbf{j} - \mathbf{k}\).
- Here, \( \mathbf{i}, \mathbf{j}, \mathbf{k} \) are the unit vectors along the x, y, and z axes respectively.
- **Vector v** is represented as \(\mathbf{i} - \mathbf{k}\).
**Objective:**
1. Calculate the cross product **u × v**.
2. Calculate the cross product **v × u**.
3. Determine the length (magnitude) of each cross product.
4. Identify the direction for each vector cross product using the right-hand rule.
**Note:** The cross product of two vectors results in a vector that is perpendicular to the plane formed by the original vectors.
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