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
![### Problem Statement
a) Find \(|\mathbf{v}|\) if \(\mathbf{v} = -7\mathbf{i} - 6\mathbf{j}\). Give the exact value.
b) Graph the vector \(\mathbf{v}\) in the coordinate plane.
### Explanation
- **Part (a): Magnitude of the Vector**
- The vector \(\mathbf{v}\) is given by \(-7\mathbf{i} - 6\mathbf{j}\).
- The magnitude of \(\mathbf{v}\), denoted as \(|\mathbf{v}|\), is calculated using the formula for the magnitude of a vector:
\[
|\mathbf{v}| = \sqrt{(-7)^2 + (-6)^2}
\]
- **Part (b): Graphing the Vector**
- To graph \(\mathbf{v} = -7\mathbf{i} - 6\mathbf{j}\), plot the point \((-7, -6)\) on the coordinate plane.
- The vector originates from the origin \((0, 0)\) and points to the coordinates \((-7, -6)\). Use an arrow to indicate the direction of the vector.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd4248fea-c75e-4e96-a274-f1cd3c8da07a%2Fb056006c-6149-4e70-8f5f-ae2a72e872c8%2Fg2pvy1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
a) Find \(|\mathbf{v}|\) if \(\mathbf{v} = -7\mathbf{i} - 6\mathbf{j}\). Give the exact value.
b) Graph the vector \(\mathbf{v}\) in the coordinate plane.
### Explanation
- **Part (a): Magnitude of the Vector**
- The vector \(\mathbf{v}\) is given by \(-7\mathbf{i} - 6\mathbf{j}\).
- The magnitude of \(\mathbf{v}\), denoted as \(|\mathbf{v}|\), is calculated using the formula for the magnitude of a vector:
\[
|\mathbf{v}| = \sqrt{(-7)^2 + (-6)^2}
\]
- **Part (b): Graphing the Vector**
- To graph \(\mathbf{v} = -7\mathbf{i} - 6\mathbf{j}\), plot the point \((-7, -6)\) on the coordinate plane.
- The vector originates from the origin \((0, 0)\) and points to the coordinates \((-7, -6)\). Use an arrow to indicate the direction of the vector.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 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