Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) (3, -5, -2), -2 2 5 5 (a) parametric equations (Enter your answers as a comma-separated list.) 17t 5 3 (b) symmetric equations X y z + 2 17 27 15 3-x=y=2+2 = 17 15 3 - x v+5=2+2 17 27 X-3 y-5 15 27 = = Z 15 15
Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) (3, -5, -2), -2 2 5 5 (a) parametric equations (Enter your answers as a comma-separated list.) 17t 5 3 (b) symmetric equations X y z + 2 17 27 15 3-x=y=2+2 = 17 15 3 - x v+5=2+2 17 27 X-3 y-5 15 27 = = Z 15 15
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Finding Sets of Parametric and Symmetric Equations of a Line**
**Problem Statement:**
Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). For each line, write the direction numbers as integers.
**Given Points:**
- Point 1: \((3, -5, -2)\)
- Direction Vector: \(\left(-\frac{2}{5}, \frac{2}{5}, 1\right)\)
**(a) Parametric Equations:**
Enter your answers as a comma-separated list.
**Equations:**
\[
\left(3 - \frac{17t}{5}, \ \ \ \right)
\]
**(b) Symmetric Equations:**
Select the correct set of symmetric equations from the options below:
1. \(\frac{x}{17} = \frac{y}{27} = \frac{z + 2}{15}\)
2. \(\frac{3 - x}{17} = y = \frac{z + 2}{15}\)
3. \(\frac{3 - x}{17} = \frac{y + 5}{27} = \frac{z + 2}{15}\)
4. \(\frac{x - 3}{15} = \frac{y - 5}{27} = \frac{z}{15}\)
These equations represent the line in both parametric and symmetric forms given the initial point and direction vector. Solve and choose the appropriate equations based on the given conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29b5f486-adb3-4cc3-b768-2d8a64fa9dd5%2F6a0eed79-15f7-47d9-a06c-98292b38ae82%2Fqzeoywu_processed.png&w=3840&q=75)
Transcribed Image Text:**Finding Sets of Parametric and Symmetric Equations of a Line**
**Problem Statement:**
Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). For each line, write the direction numbers as integers.
**Given Points:**
- Point 1: \((3, -5, -2)\)
- Direction Vector: \(\left(-\frac{2}{5}, \frac{2}{5}, 1\right)\)
**(a) Parametric Equations:**
Enter your answers as a comma-separated list.
**Equations:**
\[
\left(3 - \frac{17t}{5}, \ \ \ \right)
\]
**(b) Symmetric Equations:**
Select the correct set of symmetric equations from the options below:
1. \(\frac{x}{17} = \frac{y}{27} = \frac{z + 2}{15}\)
2. \(\frac{3 - x}{17} = y = \frac{z + 2}{15}\)
3. \(\frac{3 - x}{17} = \frac{y + 5}{27} = \frac{z + 2}{15}\)
4. \(\frac{x - 3}{15} = \frac{y - 5}{27} = \frac{z}{15}\)
These equations represent the line in both parametric and symmetric forms given the initial point and direction vector. Solve and choose the appropriate equations based on the given conditions.
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