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Suppose ū = (4, 1, 1) and ū = (2, -5, –3). Then:

Suppose ū = (4, 1, 1) and ū = (2, -5, –3). Then:

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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## Vector Operations Problem **Problem Statement:** Suppose \(\bar{u} = \langle 4, 1, 1 \rangle\) and \(\bar{v} = \langle 2, -5, -3 \rangle\). Then: 1. \( \bar{u} + \bar{v} = \) _________ 2. \( \bar{u} - \bar{v} = \) _________ 3. \( \bar{v} - \bar{u} = \) _________ 4. \( 2\bar{u} = \) _________ 5. \( -\frac{1}{5}\bar{v} = \) _________ 6. \( 5\bar{u} - 6\bar{v} = \) _________ **Explanation:** 1. **Addition of Vectors**: - \( \bar{u} + \bar{v} \) involves adding corresponding components of \(\bar{u}\) and \(\bar{v}\). 2. **Subtraction of Vectors**: - \( \bar{u} - \bar{v} \) involves subtracting corresponding components of \(\bar{v}\) from \(\bar{u}\). 3. **Subtraction of Vectors (Reversed)**: - \( \bar{v} - \bar{u} \) involves subtracting corresponding components of \(\bar{u}\) from \(\bar{v}\). 4. **Scalar Multiplication**: - \( 2\bar{u} \) involves multiplying each component of \( \bar{u} \) by 2. 5. **Scalar Multiplication with Negative Fraction**: - \( -\frac{1}{5}\bar{v} \) involves multiplying each component of \(\bar{v}\) by \(-\frac{1}{5}\). 6. **Linear Combination of Vectors**: - \( 5\bar{u} - 6\bar{v} \) involves multiplying each component of \(\bar{u}\) by 5 and each component of \(\bar{v}\) by \(-6\), and then adding the resulting vectors. **Diagrams:** No diagrams are present in the image. The tasks
Transcribed Image Text:## Vector Operations Problem **Problem Statement:** Suppose \(\bar{u} = \langle 4, 1, 1 \rangle\) and \(\bar{v} = \langle 2, -5, -3 \rangle\). Then: 1. \( \bar{u} + \bar{v} = \) _________ 2. \( \bar{u} - \bar{v} = \) _________ 3. \( \bar{v} - \bar{u} = \) _________ 4. \( 2\bar{u} = \) _________ 5. \( -\frac{1}{5}\bar{v} = \) _________ 6. \( 5\bar{u} - 6\bar{v} = \) _________ **Explanation:** 1. **Addition of Vectors**: - \( \bar{u} + \bar{v} \) involves adding corresponding components of \(\bar{u}\) and \(\bar{v}\). 2. **Subtraction of Vectors**: - \( \bar{u} - \bar{v} \) involves subtracting corresponding components of \(\bar{v}\) from \(\bar{u}\). 3. **Subtraction of Vectors (Reversed)**: - \( \bar{v} - \bar{u} \) involves subtracting corresponding components of \(\bar{u}\) from \(\bar{v}\). 4. **Scalar Multiplication**: - \( 2\bar{u} \) involves multiplying each component of \( \bar{u} \) by 2. 5. **Scalar Multiplication with Negative Fraction**: - \( -\frac{1}{5}\bar{v} \) involves multiplying each component of \(\bar{v}\) by \(-\frac{1}{5}\). 6. **Linear Combination of Vectors**: - \( 5\bar{u} - 6\bar{v} \) involves multiplying each component of \(\bar{u}\) by 5 and each component of \(\bar{v}\) by \(-6\), and then adding the resulting vectors. **Diagrams:** No diagrams are present in the image. The tasks
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