   Chapter 12.1, Problem 16E

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 ( 1 , − 6 , 8 ) , Q ( − 3 , − 2 , 5 )

To determine

To calculate: The line segment from P(1,6,8)and Q(3,2,5) by a vector valued function and by a set of parametric equation.

Explanation

Given:

The points are P(1,6,8)and Q(3,2,5).

Formula used:

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

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

Where t varies from 0 to 1.

Calculation:

Consider the point P(1,6,8) as r0 and the point Q(3,2,5) as r1.

r0=(1,6,8)=i6j+8k

And,

r1=(3,2,5)=3i2j+5k

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

r=(1t)r0+tr1 …...…... (1)

Where t varies from 0 to 1

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