   Chapter 12.1, Problem 36E

Chapter
Section
Textbook Problem

# Sketching a Space CurveIn Exercises 31–38, sketch the space curve represented by the vector-valued function and give the orientation of the curve. r ( t ) = t 2 i + 2 t j + 3 2 t k

To determine

To graph: The space curve represented by the vector value function, r(t) = t2 i+ 2t j+32t k.

Explanation

Given:

The vector value function, r(t) = t2 i+ 2t j+32t k.

Graph:

Consider the provided vector value function,

r(t) = t2 i+ 2t j+32t k

Here,

x=t2 …...…... (1)

y=2t …...…... (2)

z=32t …...…... (3)

From equation (2), t=y2, therefore substitute this value in equation (1) and (3).

x=(y2)2=y24

And

z=32t=32(y2)=34y

Make the space curve of the provided vector equation by the use of maple software:

Input:

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