   Chapter 12.1, Problem 62E

Chapter
Section
Textbook Problem

# Sketching a CurveShow that the vector-valued function r ( t ) = e − t cos t i + e − t sin t j + e − t k lies on the cone z 2 = x 2 + y 2 . Sketch the curve.

To determine

To Calculate: The vector valued function lie on the cone.

Explanation

Given: r(t)=etcost i+ etsint j+et k

Calculation:

From the provided function the components of the function are, <etcost,etsint,et> so,

x=etcost,y=etsint,z=et

xet=cost,yet=sint,z=et

xz=cost

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