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?

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter8: Introduction To Functions
Section8.4: The Slope-intercept Form Of A Linear Equation
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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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