   Chapter 12.1, Problem 13E

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(0,0,0), Q(3,1,2)

To determine

To calculate: The line segment joining the point P(0,0,0) and Q(3,1,2) by a vector valued function and a set of parametric equation.

Explanation

Given:

The provided points are P(0,0,0) and Q(3,1,2).

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(0,0,0) as r0 and the point Q(3,1,2) as r1 from the origin.

Then,

r0=0,0,0=0i+0j+0k

And,

r1=3,1,2=5i+2j+2k

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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