d Perform the following Operations on the | 14 = (-2₁-3₁-5), V = (4₁-2₁-1) to W² = (-404) R₁W = [ (u ² √²)ū² = ¯ (( W. WIR ) · U² = [ @²₁ √² + V².W = [
d Perform the following Operations on the | 14 = (-2₁-3₁-5), V = (4₁-2₁-1) to W² = (-404) R₁W = [ (u ² √²)ū² = ¯ (( W. WIR ) · U² = [ @²₁ √² + V².W = [
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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Can anyone please help me to solve this problem ? I am stuck!
![**Problem:**
Perform the following operations on the vectors:
\[
\vec{u} = \langle 2, -3, 5 \rangle, \quad \vec{v} = \langle 4, -2, -1 \rangle, \quad \vec{w} = \langle -4, 0, 4 \rangle
\]
1. \(\vec{u} \cdot \vec{w} = \_\_\_\_\)
2. \(((\vec{u} \cdot \vec{w}) \cdot \vec{u}) / \vec{u} = \_\_\_\_\)
3. \(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} = \_\_\_\_\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2F2b7d91ac-ff8a-4aee-b297-9f9108a99958%2Fnwlrk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Perform the following operations on the vectors:
\[
\vec{u} = \langle 2, -3, 5 \rangle, \quad \vec{v} = \langle 4, -2, -1 \rangle, \quad \vec{w} = \langle -4, 0, 4 \rangle
\]
1. \(\vec{u} \cdot \vec{w} = \_\_\_\_\)
2. \(((\vec{u} \cdot \vec{w}) \cdot \vec{u}) / \vec{u} = \_\_\_\_\)
3. \(\vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} = \_\_\_\_\)
![### Problem
Perform the following operations on the vectors:
**\[ \vec{u} = \langle -2, 3, -5 \rangle \]**
**\[ \vec{v} = \langle 4, -2, 1 \rangle \]**
**\[ \vec{w} = \langle -4, 0, 4 \rangle \]**
1. **\[ \vec{u} \cdot \vec{w} = \]**
- Calculate the dot product of vectors \(\vec{u}\) and \(\vec{w}\).
2. **\[ (\vec{u} \cdot \vec{v}) \cdot \vec{u} = \]**
- First, find the dot product of \(\vec{u}\) and \(\vec{v}\).
- Then multiply the resulting scalar by vector \(\vec{u}\).
3. **\[ ((\vec{w} \cdot \vec{w}) \cdot \vec{u}) \cdot \vec{u} = \]**
- Calculate the dot product of \(\vec{w}\) with itself.
- Multiply the result by vector \(\vec{u}\).
- Then find the dot product of the resulting vector with \(\vec{u}\).
4. **\[ \vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} = \]**
- Calculate the dot product of vectors \(\vec{u}\) and \(\vec{v}\).
- Calculate the dot product of vectors \(\vec{v}\) and \(\vec{w}\).
- Add the two results.
Fill in the boxes with the answers obtained from the calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99d15f92-0bff-4b4d-a47e-2ac33d144271%2F2b7d91ac-ff8a-4aee-b297-9f9108a99958%2F9hwxqip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem
Perform the following operations on the vectors:
**\[ \vec{u} = \langle -2, 3, -5 \rangle \]**
**\[ \vec{v} = \langle 4, -2, 1 \rangle \]**
**\[ \vec{w} = \langle -4, 0, 4 \rangle \]**
1. **\[ \vec{u} \cdot \vec{w} = \]**
- Calculate the dot product of vectors \(\vec{u}\) and \(\vec{w}\).
2. **\[ (\vec{u} \cdot \vec{v}) \cdot \vec{u} = \]**
- First, find the dot product of \(\vec{u}\) and \(\vec{v}\).
- Then multiply the resulting scalar by vector \(\vec{u}\).
3. **\[ ((\vec{w} \cdot \vec{w}) \cdot \vec{u}) \cdot \vec{u} = \]**
- Calculate the dot product of \(\vec{w}\) with itself.
- Multiply the result by vector \(\vec{u}\).
- Then find the dot product of the resulting vector with \(\vec{u}\).
4. **\[ \vec{u} \cdot \vec{v} + \vec{v} \cdot \vec{w} = \]**
- Calculate the dot product of vectors \(\vec{u}\) and \(\vec{v}\).
- Calculate the dot product of vectors \(\vec{v}\) and \(\vec{w}\).
- Add the two results.
Fill in the boxes with the answers obtained from the calculations.
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