   Chapter 10.6, Problem 31E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Explain why the lines below are coincident. l 1 : x ,   y ,   z = 0 ,   0 ,   0 + n 1 ,   2 ,   - 3 and l 2 : x ,   y ,   z = 1 ,   2 ,   - 3 + r - 1 ,   - 2 ,   3

To determine

To explain:

The reason for the given lines to be coincident.

Explanation

The given two lines are,

𝓁1: x, y, z=0, 0, 0+n1, 2, -3 and

𝓁2: x, y, z=1, 2, -3+r-1, -2, 3

Definition for coincident lines.

Two lines are said to be coincident if they have a common point and their direction vectors are multiples of each other.

We have to check whether there is any common point occurs for the two lines.

Write the point form of the two lines.

𝓁1=0+n, 0+2n, 0-3n

It can be written as,

𝓁1=n, 2n, -3n

𝓁2=1-r, 2-2r, -3+3r

If there is a common point for the two lines, then

n=1-r

2n=2-2r

-3n=-3+3r

From first equation, r=1-n

Substitute this value in second equation.

2n=2-21-n

Multiplying,

2n=2-2-2n

Combining the like terms,

2n+2n=2-2

Simplifying,

4n=0

From this,

n=0

Substitute n=0 in r=1-n.

r=1-0

Simplifying,

r=1

Substitute n=0 and r=1 in the point form of the line equations

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

Simplify the expressions in Exercises 97106. x1/2y2x1/2y

Finite Mathematics and Applied Calculus (MindTap Course List)

If f(x)=x+x, show that lim x0 f(x) exists hut is not equal to f(2).

Single Variable Calculus: Early Transcendentals, Volume I

Let f be the function defined by f(x)={x2+1ifx0xifx0 Find f(2), f(0), and f(1).

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach 