Consider the following. r(t) = (9− t)i + (7t − 6)j + 4tk, P(8, 1, 4) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t) = √ 42 (t-1) X Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) 5s 20 (8-) + (+¹) + (+4)** +1 42 √42 42 r(t(s)) = (b) Find the point 5 units along the curve (in the direction of increasing t) from P. 5 5 20 (x, y, z) = nos - (( - ) + ( + 1) + (+4)*) 8 i+ 42 42 42
Consider the following. r(t) = (9− t)i + (7t − 6)j + 4tk, P(8, 1, 4) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t) = √ 42 (t-1) X Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) 5s 20 (8-) + (+¹) + (+4)** +1 42 √42 42 r(t(s)) = (b) Find the point 5 units along the curve (in the direction of increasing t) from P. 5 5 20 (x, y, z) = nos - (( - ) + ( + 1) + (+4)*) 8 i+ 42 42 42
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the following.
r(t) = (9 t)i + (7t − 6)j + 4tk, P(8, 1, 4)
(a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t.
42 (t-1) X
s(t) =
Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.)
S
5s
20
=
(8 - √ ₁2 ) + ( + ¹) + ( √2 + 4) k
42
42
42
r(t(s))
(b) Find the point 5 units along the curve (in the direction of increasing t) from P.
5
( (8 - √5₁2)₁ + ( √√₁2 + ¹) ₁ + (
4) k × )
42
42
(x, y, z) =
20
√42
+4k
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