:. Consider the lines L1 and L2 in R³ given by the vector equationsL1 : ở = (2,4, 4) + t(4,1, 5) and L2:0 = (1,–3, 2) + t(-2,3, 1).%3|(a) Find an expression for the distance between two points on L1 and L2. Your expressionshould be a function f: R? → R.(b) By finding the extreme values of f, find the shortest distance between L1 and L2. Besure to fully justify your answer.[Hint: The expression for the distance-squared is often simpler than the expression forthe distance. So you may find it easier to work with f2 instead of f. Ifsure to clearly explain how the process of optimizing f2 is related to optimizing f.]youdoSo,be

Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And L2 : v→ =1, -3, 2+t -2, 3, 1

Answered: Consider the lines L1 and L2 in R³…

Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and L2 : 0 = (1, –3, 2) + t(-2,3, 1).

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.2: Determinants

Problem 13AEXP

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:. Consider the lines L1 and L2 in R³ given by the vector equations
L1 : ở = (2,4, 4) + t(4,1, 5) and L2:0 = (1,–3, 2) + t(-2,3, 1).
%3|
(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
sure to clearly explain how the process of optimizing f2 is related to optimizing f.]
you
do
So,
be

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