Consider the following. r(t) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t)=√86 (t-1) Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) s(t) s(t) 6s(t) √86 √86 r(t(s)) = 4- 86 (x, y, z) = i+ 11 + +71 + X (b) Find the point 4 units along the curve (in the direction of increasing t) from P. 4 -( (4- √ 86 )₁ + ( 11 + 24 4 286 )₁ +7(1 + √56)* ) k √86 86
Consider the following. r(t) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7) (a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t. s(t)=√86 (t-1) Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.) s(t) s(t) 6s(t) √86 √86 r(t(s)) = 4- 86 (x, y, z) = i+ 11 + +71 + X (b) Find the point 4 units along the curve (in the direction of increasing t) from P. 4 -( (4- √ 86 )₁ + ( 11 + 24 4 286 )₁ +7(1 + √56)* ) k √86 86
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) = (5 t)i + (6t - 5)j + 7tk, P(4, 1, 7)
(a) Find the arc length function s(t) for the curve measured from the point P in the direction of increasing t.
√86 (t-1)
s(t) =
Reparametrize the curve with respect to arc length starting from P. (Enter your answer in terms of s.)
S
r(t(s)):
-
=
-
s(t)
√86
i+ 11 +
6s(t)
√86
j+71+
s(t)
√86
k
X
(b) Find the point 4 units along the curve (in the direction of increasing t) from P.
4
24
4
(x, y, z)
> -( (1 - √ ²56 )¹ + (11 + 355 )³ + 7 (¹ + √5) *
4-
1
k
√86
86
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