   Chapter 12.1, Problem 15E

Chapter
Section
Textbook Problem

# Writing a Vector-Valued Function In Exercises 13–16, represent the line segment from P to Q by a vector-valued function and by a set of parametric equations.P(-2,5,-3), Q(-1,4,9)

To determine

To calculate: The line segment joining the point P(2,5,3) and Q(1,4,9) by a vector valued function and a set of parametric equation.

Explanation

Given:

The provided points are P(2,5,3) and Q(1,4,9).

Formula used:

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

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

Where t varies from 0 to 1.

Calculation:

Consider the point P(2,5,3) as r0 and the point Q(1,4,9) as r1 from the origin.

Then,

r0=2,5,3=2i+5j3k

And,

r1=1,4,9=1i+4j+9k

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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