Let L₁ be the line passing through the point P₁(-5, -1, -3) with direction vector d=[3, 2, 1]T, and let L₂ be the line passing through the point P₂(1, 2, 1) with the same direction vector. 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 'V' 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, -3) with direction vector d=[3, 2, 1]T, and let L₂ be the line passing through the point P₂(1, 2, 1) with the same direction vector. 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 'V' where needed to give an exact value for your answer. d = 0 Q1 = (0, 0, 0) Q2 = (0, 0, 0)
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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Question
![Let \( L_1 \) be the line passing through the point \( P_1(-5, -1, -3) \) with direction vector \(\mathbf{d} = [3, 2, 1]^T\), and let \( L_2 \) be the line passing through the point \( P_2(1, 2, 1) \) with the same direction vector. Find the shortest distance \( d \) between these two lines, and find a point \( Q_1 \) on \( L_1 \) and a point \( Q_2 \) on \( L_2 \) so that \( d(Q_1, Q_2) = d \). Use the square root symbol ‘\(\sqrt{}\)’ where needed to give an exact value for your answer.
\[
d = 0
\]
\[
Q_1 = (0, 0, 0)
\]
\[
Q_2 = (0, 0, 0)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2b7ff9-b952-4215-9e0f-f264e2036fb8%2Fa9f99f44-b045-4429-b292-7d5b38bc1af3%2Fijne1wj_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( L_1 \) be the line passing through the point \( P_1(-5, -1, -3) \) with direction vector \(\mathbf{d} = [3, 2, 1]^T\), and let \( L_2 \) be the line passing through the point \( P_2(1, 2, 1) \) with the same direction vector. Find the shortest distance \( d \) between these two lines, and find a point \( Q_1 \) on \( L_1 \) and a point \( Q_2 \) on \( L_2 \) so that \( d(Q_1, Q_2) = d \). Use the square root symbol ‘\(\sqrt{}\)’ where needed to give an exact value for your answer.
\[
d = 0
\]
\[
Q_1 = (0, 0, 0)
\]
\[
Q_2 = (0, 0, 0)
\]
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