   Chapter 12.1, Problem 20E

Chapter
Section
Textbook Problem

# MatchingIn Exercises 19–22, match the equation with its graph. [The graphs are labeled (a), (b), (c), and (d).](a) (b) (c) (d) r ( t ) = cos ( π t ) i + sin ( π t ) j + t 2 k ,       − 1 ≤ t ≤ 1

To determine
Match the graph of the function, r(t)=cos(πt)i+sin(πt) j+t2 k from the provided four options.

Explanation

Given:

The equation r(t)=cos(πt)i+sin(πt) j+t2 k where 1t1. The graph the curve are shown below,

Explanation:

Consider the provided vector equation,

r(t)=cos(πt)i+sin(πt) j+t2 k where 1t1

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

Step1: First write the library function with(VectorCalculus):.

Step2: Define the position vector in Cartesian coordinate system,

S1:=PositionVecor([cos(πt),sin(πt),t2],cartesian)

Step3: Press Enter button

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