Consider the vector function given below. r(t) = <6t, 5 cos(t), 5 sin(t)> a) Find the unit tangent and unit normal vectors T(t) and N(t). b) Use the formula k(t)= (|T'(t)|) / (|r'(t)|) to find the curvature

Consider the vector function given below. r(t) = <6t, 5 cos(t), 5 sin(t)> a) Find the unit tangent and unit normal vectors T(t) and N(t). b) Use the formula k(t)= (|T'(t)|) / (|r'(t)|) to find the curvature

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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Question

Consider the vector function given below.

r(t) = <6t, 5 cos(t), 5 sin(t)>

a) Find the unit tangent and unit normal vectors T(t) and N(t).

b) Use the formula k(t)= (|T'(t)|) / (|r'(t)|) to find the curvature

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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