   Chapter 11.5, Problem 19E

Chapter
Section
Textbook Problem

# Finding Parametric EquationsIn Exercises 17–24, find a set of parametric equations of the line with the given characteristics.The line passes through the point ( 2 , 1 , 2 ) and is parallel to the line x = − t , y = 1 + t , z = − 2 + t .

To determine

To calculate: Find the parametric equations of the line passing through the point (2,1,2) and is parallel to the line x=t,y=1+t and z=2+t.

Explanation

Given:

The line passes through the point (2,1,2) and is parallel to the line x=t,y=1+t and z=2+t.

Formula used:

Parametric equations of a line are:

x=x1+at,y=y1+bt and z=z1+ct

Calculation:

Now as line to be obtained is parallel to the line x=t,y=1+t and z=z1+ct

Therefore, the line must also be parallel to the provided parallel vector 1,1,1.

Thus, to find a set of parametric equations of the line,

coordinates x1=2,y1=1 and z1=2

point is (2,1,2) and

direction numbers a=1,b=1 and c=1

parallel vector to the provided line is 1,1,1

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