   Chapter 13.1, Problem 30E

Chapter
Section
Textbook Problem

# Find three different surfaces that contain the curve r(t) = t2 i + ln t j + (1/t) k.

To determine

To find: The three different surfaces of the curve r(t)=t2i+lntj+(1t)k .

Explanation

Given data:

Vector equation is r(t)=t2i+lntj+(1t)k .

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 a vector function r(t)=t2i+lntj+(1t)k .

x=t2 (1)

y=lnt (2)

z=1t (3)

The domain of vector function is (0,) .

Re-arrange the parametric equation of equation (1)

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