Consider the following parametric lines and answer the questions. z = 29 - 21t, x=1+t, y = 4, x=7-2t, y = 6, z = 4 + t, x=5+3t y=3-t, z=1-7t, L₁ L₂ L3 (a). Determine whether L₁ and L2 are parallel, intersect, or are skew. If they intersect, find the intersectiong point. (b). Determine whether L₁ and L3 are parallel, intersect, or are skew. If they intersect, find the intersectiong point. (c). Determine whether L2 and L3 are parallel, intersect, or are skew. If they intersect, find the intersectiong point.
Consider the following parametric lines and answer the questions. z = 29 - 21t, x=1+t, y = 4, x=7-2t, y = 6, z = 4 + t, x=5+3t y=3-t, z=1-7t, L₁ L₂ L3 (a). Determine whether L₁ and L2 are parallel, intersect, or are skew. If they intersect, find the intersectiong point. (b). Determine whether L₁ and L3 are parallel, intersect, or are skew. If they intersect, find the intersectiong point. (c). Determine whether L2 and L3 are parallel, intersect, or are skew. If they intersect, find the intersectiong point.
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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Transcribed Image Text:### Parametric Lines and Their Relationships
**Consider the following parametric lines and answer the questions.**
**Line 1 (\(L_1\)):**
- \(x = 1 + t\)
- \(y = 4\)
- \(z = 29 - 21t\)
**Line 2 (\(L_2\)):**
- \(x = 7 - 2t\)
- \(y = 6\)
- \(z = 4 + t\)
**Line 3 (\(L_3\)):**
- \(x = 5 + 3t\)
- \(y = 3 - t\)
- \(z = 1 - 7t\)
**Questions:**
(a) Determine whether \(L_1\) and \(L_2\) are parallel, intersect, or are skew. If they intersect, find the intersection point.
(b) Determine whether \(L_1\) and \(L_3\) are parallel, intersect, or are skew. If they intersect, find the intersection point.
(c) Determine whether \(L_2\) and \(L_3\) are parallel, intersect, or are skew. If they intersect, find the intersection point.
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