   Chapter 11.5, Problem 10E

Chapter
Section
Textbook Problem

# Finding Parametric and Symmetric EquationsIn Exercises 13–16, find sets of (a) parametric equations and (b) symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) ( 0 , 4 , 3 ) , ( − 1 , 2 , 5 )

(a)

To determine

To calculation: Find the parametric equations of the line passing through two points (0,4,3) and (1,2,5).

Explanation

Given:

The line passes through two points (0,4,3) and (1,2,5).

Formula used:

The parametric equations of a line are:

x=x1+at,y=y1+bt

and z=z1+ct

Vector for two points:

v=(a2a1),(b2b1),(c2c1)

Calculation:

To find a direction vector for the line passing through P and Q

First of all let use the points P(0,4,3) and Q(1,2,5)

v=QP=(a2a1),(b2b1),(c2c1)=(0(1)),(42),(35)=1,2,2

Also let us now use the direction numbers

a=1, b=2 and c=2

(b)

To determine
The symmetric equations of the line passing through two points (0,4,3) and (1,2,5).

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