Let r(t) = w +tv be the parametrization of a line. (a) Show that the are length function s (t) = | ||r'(u)|| du is given by s(t) = t || v||. This shows that r(t) is an arc length parametrizaton if and only if v is a unit vector. (b) Find an arc length parametrization of the line with w = (1, 2, 3) and v = (3, 4, 5).

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Let r(t) = w +tv be the parametrization of a line.
(a) Show that the are length function s (t) = | ||r'(u)|| du is given
by s(t) = t || v||. This shows that r(t) is an arc length parametrizaton if
and only if v is a unit vector.
(b) Find an arc length parametrization of the line with w = (1, 2, 3)
and v
= (3, 4, 5).
Transcribed Image Text:Let r(t) = w +tv be the parametrization of a line. (a) Show that the are length function s (t) = | ||r'(u)|| du is given by s(t) = t || v||. This shows that r(t) is an arc length parametrizaton if and only if v is a unit vector. (b) Find an arc length parametrization of the line with w = (1, 2, 3) and v = (3, 4, 5).
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