   Chapter 13.1, Problem 13E

Chapter
Section
Textbook Problem

# Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.13. r(t) = t2 i + t4 j + t6 k

To determine

To sketch: the curve of vector equation r(t)=t2i+t4j+t6k and indicate the direction of increment of t.

Explanation

Given data:

Vector function is r(t)=t2i+t4j+t6k .

Definition:

Consider a vector function as r(t)=f(t)i+g(t)j+h(t)k , then parametric equations to plot space curve C are,

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

Here,

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

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

From definition, write the parametric equations of vector function r(t)=t2i+t4j+t6k .

x=t2

y=t4 (1)

z=t6 (2)

From parametric equations, it is obvious that, for any value of t when t0 the parametric equations are positive whereas, if t=0 the values of parametric equations are equal to zero

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