Let L₁ be the line passing through the point P₁(-3, 1, -2) with direction vector d=[0, -1, 2]T, and let L₂ be the line passing through the point P₂(3, 5, -5) 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(-3, 1, -2) with direction vector d=[0, -1, 2]T, and let L₂ be the line passing through the point P₂(3, 5, -5) 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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![**Problem Statement:**
Let \( L_1 \) be the line passing through the point \( P_1(-3, 1, -2) \) with direction vector \( \mathbf{d} = [0, -1, 2]^T \), and let \( L_2 \) be the line passing through the point \( P_2(3, 5, -5) \) 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.
**Solution:**
- Shortest distance, \( d \):
\[
d = 0
\]
- Point \( Q_1 \) on \( L_1 \):
\[
Q_1 = (0, 0, 0)
\]
- Point \( Q_2 \) on \( L_2 \):
\[
Q_2 = (0, 0, 0)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec2b7ff9-b952-4215-9e0f-f264e2036fb8%2F6d576fe8-43ff-4d80-89a1-2d977d734e9e%2Fqaf71hi_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Let \( L_1 \) be the line passing through the point \( P_1(-3, 1, -2) \) with direction vector \( \mathbf{d} = [0, -1, 2]^T \), and let \( L_2 \) be the line passing through the point \( P_2(3, 5, -5) \) 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.
**Solution:**
- Shortest distance, \( d \):
\[
d = 0
\]
- Point \( Q_1 \) on \( L_1 \):
\[
Q_1 = (0, 0, 0)
\]
- Point \( Q_2 \) on \( L_2 \):
\[
Q_2 = (0, 0, 0)
\]
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