   Chapter 12.1, Problem 14E

Chapter
Section
Textbook Problem

# Writing a Vector-Valued FunctionIn Exercises 13–16, represent the line segment from P to Q by a vector-valued function and by a set of parametric equations. P ( 0 , 2 , − 1 ) , Q ( 4 , 7 , 2 )

To determine

To calculate: The line segment from P(0,2,1)to Q(4,7,2) by a vector valued function and by a set of parametric equation.

Explanation

Given:

The provided points are P(0,2,1)and Q(4,7,2).

Formula used:

The vector equation of a line between the points r0 and r1 is represented by

r(t)=(1t)r0+tr1

Where, t varies from 0 to 1.

Calculation:

Consider the point P(0,2,1) as r0 and the point Q(4,7,2) as r1.

r0=(0,2,1)=0i+2j1k

And,

r1=(4,7,2)=4i+7j+2k

The vector equation of a line between the points r0 and r1 is,

r=(1t)r0+tr1

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