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
![**Finding the Point of Intersection**
To find the point of intersection between two lines represented in their parametric forms, we consider the two lines \( L_1 \) and \( L_2 \) given by:
\[ L_1: \frac{x - 17}{3} = \frac{y - 58}{8} = \frac{z - 23}{2} \]
\[ L_2: \frac{x - 49}{7} = \frac{y - 26}{4} = z - 15 \]
The goal is to determine the point \((x, y, z)\) at which these two lines intersect. The method involves solving the system of equations that represent the lines.
1. **Translate Parametric Forms to System of Equations:**
For \( L_1 \):
\[
\begin{cases}
x = 17 + 3t \\
y = 58 + 8t \\
z = 23 + 2t
\end{cases}
\]
where \( t \) is a parameter specific to \( L_1 \).
For \( L_2 \):
\[
\begin{cases}
x = 49 + 7s \\
y = 26 + 4s \\
z = 15 + s
\end{cases}
\]
where \( s \) is a parameter specific to \( L_2 \).
2. **Equating Both Sets of Parametric Equations:**
To find the intersection, we set \( x \), \( y \), and \( z \) from \( L_1 \) equal to \( x \), \( y \), and \( z \) from \( L_2 \):
\[
\begin{cases}
17 + 3t = 49 + 7s \\
58 + 8t = 26 + 4s \\
23 + 2t = 15 + s
\end{cases}
\]
3. **Solve the System of Equations:**
Now solve these equations simultaneously to find the values of \( t \) and \( s \).
The steps will generally involve:
- Isolating one variable in one of the equations to find a relation between \( t \) and](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2eee30e-7760-4146-894b-912e2799cdb0%2F3fc69ba3-8e85-48cd-8a3e-bd2d6ed0f60d%2Ff6chqh8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Point of Intersection**
To find the point of intersection between two lines represented in their parametric forms, we consider the two lines \( L_1 \) and \( L_2 \) given by:
\[ L_1: \frac{x - 17}{3} = \frac{y - 58}{8} = \frac{z - 23}{2} \]
\[ L_2: \frac{x - 49}{7} = \frac{y - 26}{4} = z - 15 \]
The goal is to determine the point \((x, y, z)\) at which these two lines intersect. The method involves solving the system of equations that represent the lines.
1. **Translate Parametric Forms to System of Equations:**
For \( L_1 \):
\[
\begin{cases}
x = 17 + 3t \\
y = 58 + 8t \\
z = 23 + 2t
\end{cases}
\]
where \( t \) is a parameter specific to \( L_1 \).
For \( L_2 \):
\[
\begin{cases}
x = 49 + 7s \\
y = 26 + 4s \\
z = 15 + s
\end{cases}
\]
where \( s \) is a parameter specific to \( L_2 \).
2. **Equating Both Sets of Parametric Equations:**
To find the intersection, we set \( x \), \( y \), and \( z \) from \( L_1 \) equal to \( x \), \( y \), and \( z \) from \( L_2 \):
\[
\begin{cases}
17 + 3t = 49 + 7s \\
58 + 8t = 26 + 4s \\
23 + 2t = 15 + s
\end{cases}
\]
3. **Solve the System of Equations:**
Now solve these equations simultaneously to find the values of \( t \) and \( s \).
The steps will generally involve:
- Isolating one variable in one of the equations to find a relation between \( t \) and
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
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