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...
Related questions
Question
3
![**Problem Statement:**
3) Let \(\vec{a} = 2\vec{i} + \vec{j}\), \(\vec{b} = 5\vec{i} - 4\vec{j}\) and \(\vec{c} = \vec{i} + \vec{j}\) be vectors in 2D. Simplify \(\vec{a} + \vec{b} + 3\vec{c}\) and write in component form.
**Solution:**
Given:
- \(\vec{a} = 2\vec{i} + \vec{j}\)
- \(\vec{b} = 5\vec{i} - 4\vec{j}\)
- \(\vec{c} = \vec{i} + \vec{j}\)
First, compute \(3\vec{c}\):
\[
3\vec{c} = 3(\vec{i} + \vec{j}) = 3\vec{i} + 3\vec{j}
\]
Now, add \(\vec{a}\), \(\vec{b}\), and \(3\vec{c}\):
\[
\vec{a} + \vec{b} + 3\vec{c} = (2\vec{i} + \vec{j}) + (5\vec{i} - 4\vec{j}) + (3\vec{i} + 3\vec{j})
\]
Combine the components:
- \(i\)-components: \(2 + 5 + 3 = 10\)
- \(j\)-components: \(1 - 4 + 3 = 0\)
Thus, the simplified vector in component form is:
\[
10\vec{i} + 0\vec{j} = 10\vec{i}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f85931-ed68-43c6-82f9-075f499bfced%2F2d74fccd-446d-4ede-905b-9097d25e245f%2Fcskglm_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
3) Let \(\vec{a} = 2\vec{i} + \vec{j}\), \(\vec{b} = 5\vec{i} - 4\vec{j}\) and \(\vec{c} = \vec{i} + \vec{j}\) be vectors in 2D. Simplify \(\vec{a} + \vec{b} + 3\vec{c}\) and write in component form.
**Solution:**
Given:
- \(\vec{a} = 2\vec{i} + \vec{j}\)
- \(\vec{b} = 5\vec{i} - 4\vec{j}\)
- \(\vec{c} = \vec{i} + \vec{j}\)
First, compute \(3\vec{c}\):
\[
3\vec{c} = 3(\vec{i} + \vec{j}) = 3\vec{i} + 3\vec{j}
\]
Now, add \(\vec{a}\), \(\vec{b}\), and \(3\vec{c}\):
\[
\vec{a} + \vec{b} + 3\vec{c} = (2\vec{i} + \vec{j}) + (5\vec{i} - 4\vec{j}) + (3\vec{i} + 3\vec{j})
\]
Combine the components:
- \(i\)-components: \(2 + 5 + 3 = 10\)
- \(j\)-components: \(1 - 4 + 3 = 0\)
Thus, the simplified vector in component form is:
\[
10\vec{i} + 0\vec{j} = 10\vec{i}
\]
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning