   Chapter 13.1, Problem 29E

Chapter
Section
Textbook Problem

# Find three different surfaces that contain the curve r(t) = 2t i + et j + e2t k.

To determine

To find: The three surfaces of curve r(t)=2ti+etj+e2tk .

Explanation

Given data:

Vector equation as r(t)=2ti+etj+e2tk .

Definition:

Consider a vector function such as r(t)=f(t)i+g(t)j+h(t)k . Then the parametric equations for space curve C are,

x=f(t)y=g(t)z=h(t)

Here,

f(t) , g(t) , and h(t) are components functions of r(t) , and

x, y, and z are parametric equations of space curve C.

From definition, write the parametric equations of vector function r(t)=2ti+etj+e2tk .

x=2t (1)

y=et (2)

z=e2t (3)

Re-arrange equation (1)

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