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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?

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
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?
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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