   Chapter 12.5, Problem 7E

Chapter
Section
Textbook Problem

# Find parametric equations and symmetric equations for the line.7. The line through the points (0, 1 2 , 1) and (2, 1. −3)

To determine

To find: The parametric equations for the line through the points (0,12,1) and (2,1,3) and the symmetric equations for the line through the points (0,12,1) and (2,1,3) .

Explanation

Formula:

Write the expressions to find the parametric equations for a line through the point (x0,y0,z0) and parallel to the direction vector a,b,c .

x=x0+at,y=y0+bt,z=z0+ct (1)

Write the expression to find direction vector (v) for the line through the points P0(x0,y0,z0) and P1(x1,y1,z1) .

a,b,c=(x1x0),(y1y0),(z1z0) (2)

Write the expressions to find the symmetric equations for a line through the point (x0,y0,z0) and parallel to the direction vector a,b,c .

xx0a=yy0b=zz0c (3)

Calculation of direction vector (v) :

Consider the points P0 is (0,12,1) and P1 is (2,1,3) .

In equation (2), substitute 0 for x0 , 12 for y0 , 1 for z0 , 2 for x1 , 1 for y1 , and 3 for z1

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 