   Chapter 11.5, Problem 20E

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 ( − 6 , 0 , 8 ) and is parallel to the line x = 5 − 2 t , y = − 4 + 2 t , z = 0.

To determine

To calculate: Find the parametric equations of the line passing through the point (6,0,8) and is parallel to the line x=52t,y=4+2t and z=0.

Explanation

Given:

The line passes through the point (6,0,8) and is parallel to the line x=52t,y=4+2t and z=0.

Formula used:

Parametric equations of a line are:

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

Calculation:

As line to be obtained is parallel to the line x=52t,y=4+2t and z=0,

Therefore, the line must also be parallel to the provided vector 2,2,0.

Now further to find a set of parametric equations of the line,

coordinates x1=6,y1=0 and z1=8

point is (6,0,8) and

direction numbers a=2,b=2 and c=0

parallel vector to the provided line is 2,2,0

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