   Chapter 10.6, Problem 27E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Which point(s) lie on the line x ,   y ,   z = 2 ,   - 1 ,   5 + n 1 ,   2 ,   - 1 ? a) 1 ,   - 3 ,   4 b) 5 ,   5 ,   2

To determine

To find:

The point(s) lie on the line x, y, z=2, -1, 5+n1, 2, -1.

Explanation

The given line is x, y, z=2, -1, 5+n1, 2, -1.

Write the point form of the line.

x, y, z=2+n, -1+2n, 5-n

From this,

x=2+n

y=-1+2n

z=5-n

Consider both the options and substitute the values of x, y, z.

When substituting a point, the value of n for the variables x, y, z must be same.

If they are same, then the corresponding point lie on the line.

Let us take option a) 1, -3, 4

Here x=1, y=-3, and z=4.

Substituting the value of x.

1=2+n

Simplifying,

n=1-2

n=1

Substituting the value of y.

-3=-1+2n

Simplifying,

2n=-3+1

2n=-2

From this,

n=-1

Substituting the value of z

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