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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.5: Applications

Problem 2EQ

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2. Let C be the path given by a smooth vector valued function
r(t) = f(t)i+ g(t)j+ h(t)k, a <ts6
be a where a, b are non-negative constants. Let k(x, y, z) be a continuous scalar
function defined over R. Use this information to answer the following questions.
a) Consider the path
C : 1(t) = r(21), sis
a
is it always the case that
|k(x, y, z) ds =
| k(x, y, z) ds?
C1
Justify your answer.
b) Consider the path
C2 : r1(t) = r(t*), Vast< vo,
is it always the case that
|k(2, y, z) ds =
1 k(x, y, z) ds?
C2
Justify your answer.

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