   Chapter 10.6, Problem 28E ### 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 ,   - 3 + n 3 ,   2 ,   - 4 ? a) 2 ,   1 ,   - 3 b) 8 ,   5 ,   - 11

To determine

To find:

The point(s) lie on the line x, y, z=2, 1, -3+n3, 2, -4.

Explanation

The given line is x, y, z=2, 1, -3+n3, 2, -4.

In this equation,

2, 1, -3 is a point on the line.

3, 2, -4 is the direction vector.

Write the point form of the line.

x, y, z=2+3n, 1+2n, -3-4n

From this,

x=2+3n

y=1+2n

z=-3-4n

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) 2, 1, -3

This point is same as the point given in the line.

Hence, this point lie on the line.

Let us take option b) 8, 5, -11

Here x=8, y=5, and z=-11

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