   Chapter 11.5, Problem 12E

Chapter
Section
Textbook Problem

# Finding Parametric and Symmetric Equations In 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 , 0 , 25 ) , ( 10 , 10 , 0 )

(a)

To determine

To calculate: Find the parametric equations of the line passing passes through

points (0,0,25) and (10,10,0).

Explanation

Given:

The line passes through two points (0,0,25) and (10,10,0).

Formula used:

Symmetric equations of a line are:

xx1a=yy1b=zz1c

Vector for two points:

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

Calculation:

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

Let us first use the points (0,0,25) and (10,10,0)

v=QP=(a2a1),(b2b1),(c2c1)=(010),(010),(250)=10,10,25

Hence let us now use the direction numbers

a=10, b=10 and c=25

(b)

To determine

To calculate: The symmetric equation of the line that passes through two points (0,0,25) and (10,10,0)

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