By finding the extreme values of f, find the shortest distance between Lị and L2. Be sure to fully justify your answer. [Hint: The expression for the distance-squared is often simpler than the expression for the distance. So you may find it easier to work with f² instead of f. If you do so, be sure to clearly explain how the process of optimizing f2 is related to optimizing f.]
By finding the extreme values of f, find the shortest distance between Lị and L2. Be sure to fully justify your answer. [Hint: The expression for the distance-squared is often simpler than the expression for the distance. So you may find it easier to work with f² instead of f. If you do so, be sure to clearly explain how the process of optimizing f2 is related to optimizing f.]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please solve (b)
![Q2. Consider the lines L1 and L2 in R3 given by the vector equations
L1 :0 = (2,4, 4)+t(4, 1, 5) and L2:ở= (1,–3, 2) + t(-2,3, 1).
(a) Find an expression for the distance between two points on L1 and L2. Your expression
should be a function f: R² → R.
(b) By finding the extreme values of f, find the shortest distance between Lị and L2. Be
sure to fully justify your answer.
[Hint: The expression for the distance-squared is often simpler than the expression for
the distance. So you may find it easier to work with f instead of f. If you do so, be
sure to clearly explain how the process of optimizing f2 is related to optimizing f.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2Fbd8c06fd-3b59-4a26-b7b3-72fb86cb09fb%2Fg4wmm2m_processed.png&w=3840&q=75)
Transcribed Image Text:Q2. Consider the lines L1 and L2 in R3 given by the vector equations
L1 :0 = (2,4, 4)+t(4, 1, 5) and L2:ở= (1,–3, 2) + t(-2,3, 1).
(a) Find an expression for the distance between two points on L1 and L2. Your expression
should be a function f: R² → R.
(b) By finding the extreme values of f, find the shortest distance between Lị and L2. Be
sure to fully justify your answer.
[Hint: The expression for the distance-squared is often simpler than the expression for
the distance. So you may find it easier to work with f instead of f. If you do so, be
sure to clearly explain how the process of optimizing f2 is related to optimizing f.]
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