Consider the following vector function. r(t): (6√2t, e6t, e-6t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). 6e -6t) (6√2, 6e6t, - be √72+36e¹2t+36e -12t T(t) N(t) = = k(t) (b) Use this formula to find the curvature. √2 = 2+e¹2t X te -12t

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 33E
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Please find N(t)

Consider the following vector function.
r(t) = (6√2t, et, e-6t)
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
(6√2, 6e6t -6e-6t)
√72+36e¹21
- 12t
T(t) =
N(t)
=
k(t) =
(b) Use this formula to find the curvature.
√2
12t - 12t
te
+36e
2 + e
Transcribed Image Text:Consider the following vector function. r(t) = (6√2t, et, e-6t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). (6√2, 6e6t -6e-6t) √72+36e¹21 - 12t T(t) = N(t) = k(t) = (b) Use this formula to find the curvature. √2 12t - 12t te +36e 2 + e
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