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Let L₁ be the line passing through the point P₁=(5, −1, −14) with direction vector №₁=[0, −1, −2]¹, and let L₂ be the line passing through the point P₂=(0, −5, −5) with direction vector ₹2=[1, −3, −4]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)

Let L₁ be the line passing through the point P₁=(5, −1, −14) with direction vector №₁=[0, −1, −2]¹, and let L₂ be the line passing through the point P₂=(0, −5, −5) with direction vector ₹2=[1, −3, −4]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
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=(5, −1, −14) with direction vector ₁=[0,-1, -2]T, and let L2 be the line passing through the point P₂=(0, −5, −5) with direction vector ₹2=[1, −3, −4]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)
Transcribed Image Text:Let L₁ be the line passing through the point P₁=(5, −1, −14) with direction vector ₁=[0,-1, -2]T, and let L2 be the line passing through the point P₂=(0, −5, −5) with direction vector ₹2=[1, −3, −4]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)
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