   Chapter 11.5, Problem 17E

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 ( 5 , − 3 , − 4 ) and is parallel to v = 〈 2 , − 1 , 3 〉 .

To determine

To calculate: Find the parametric equations of the line passing through the point (5,3,4) and is parallel to the vector v=2,1,3.

Explanation

Given:

The line passes through the point

(5,3,4) and is parallel to the vector v=2,1,3.

Formula used:

Parametric equations of a line are:

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

Calculation:

Let us first find a set of parametric equations of the line,

Coordinates x1=5,y1=3 and z1=4

Point (5,3,4) and

Direction numbers a=2,b=1 and

c=3

Parallel vector v=2,1,3.

Hence the parametric equations of a line are:

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

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