Let L₁ be the line passing through the point P₁=(11, 9, 3) with direction vector ₁-[2, 2, 2]T, and let L₂ be the line passing through the point P₂=(−1, 13, −7) with direction vector d2=[−1, 0, 1]T. Find the shortest distance d between these two lines, and find a point Q₁ on L₁ and a point Q₂ on L₂ so that d(Q₁,Q₂) = d. Use the square root symbol '√' where needed to give an exact value for your answer. d = 0 Q₁ = (0, 0, 0) Q₂ = (0, 0, 0)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 18EQ
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Let L₁ be the line passing through the point P₁=(11, 9, 3) with direction vector ₁=[2, 2, 2]¹, and let
L₂ be the line passing through the point P₂=(−1, 13, −7) with direction vector d2=[−1, 0, 1]¹.
Find the shortest distance d between these two lines, and find a point Q₁ on L₁ and a point Q₂ on
L₂ so that d(Q₁,Q2) = d. Use the square root symbol '√' where needed to give an exact value for
your answer.
d = 0
Q₁ = (0, 0, 0)
Q₂ = (0, 0, 0)
Transcribed Image Text:Let L₁ be the line passing through the point P₁=(11, 9, 3) with direction vector ₁=[2, 2, 2]¹, and let L₂ be the line passing through the point P₂=(−1, 13, −7) with direction vector d2=[−1, 0, 1]¹. Find the shortest distance d between these two lines, and find a point Q₁ on L₁ and a point Q₂ on L₂ so that d(Q₁,Q2) = d. Use the square root symbol '√' where needed to give an exact value for your answer. d = 0 Q₁ = (0, 0, 0) Q₂ = (0, 0, 0)
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