'. Consider the lines L1 and L2 in R3 given by the vector equations L1 :0 = (2,4, 4) + t(4, 1,5) and L2 :0 = (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: R? → R. (b) By finding the extreme values of f, find the shortest distance between L1 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.]
'. Consider the lines L1 and L2 in R3 given by the vector equations L1 :0 = (2,4, 4) + t(4, 1,5) and L2 :0 = (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: R? → R. (b) By finding the extreme values of f, find the shortest distance between L1 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 correctly, neat and clean work
!['. Consider the lines L1 and L2 in R given by the vector equations
L1 :0 = (2, 4, 4) +t(4, 1,5) and L2 : 0 = (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 L1 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.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0719dc05-02f0-4a27-95ad-860ae24ff415%2F39b8a27b-8529-421a-ad76-0c46c8a51ebe%2Fzoig7r6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:'. Consider the lines L1 and L2 in R given by the vector equations
L1 :0 = (2, 4, 4) +t(4, 1,5) and L2 : 0 = (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 L1 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.]
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