Consider the line L₁ described by r₁ (t) = (-t, 5+ 2t, 7 - 3t) and L₂ described by r₂(t) = (2+t, 4-3t, -7t). a. Show that L₁ and L2 are not parallel. b. Show that L₁ and L₂ are do not intersect by showing that r₁(t) = r₂ (s) has no solutions. C. What is the shortest distance between L₁ and L₂?
Consider the line L₁ described by r₁ (t) = (-t, 5+ 2t, 7 - 3t) and L₂ described by r₂(t) = (2+t, 4-3t, -7t). a. Show that L₁ and L2 are not parallel. b. Show that L₁ and L₂ are do not intersect by showing that r₁(t) = r₂ (s) has no solutions. C. What is the shortest distance between L₁ and L₂?
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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![Consider the line L₁ described by r₁ (t) = (-t, 5 + 2t, 7 - 3t) and L₂ described by r₂ (t) = (2+t, 4 - 3t, -7t).
a. Show that L₁ and L2 are not parallel.
b. Show that L₁ and L₂ are do not intersect by showing that r₁(t) = r₂ (s) has no solutions.
C. What is the shortest distance between L₁ and L₂?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44c94bd2-8c1f-4d24-8d96-8ec15a0486f1%2F220b7457-63c9-456f-8b38-1e5f756c3e0b%2Fakshe5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the line L₁ described by r₁ (t) = (-t, 5 + 2t, 7 - 3t) and L₂ described by r₂ (t) = (2+t, 4 - 3t, -7t).
a. Show that L₁ and L2 are not parallel.
b. Show that L₁ and L₂ are do not intersect by showing that r₁(t) = r₂ (s) has no solutions.
C. What is the shortest distance between L₁ and L₂?
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