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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Explain why the lines below are parallel.

l 1 : x ,   y ,   z = 2 ,   3 ,   4 + n 1 ,   2 ,   - 3 and

l 2 : x ,   y ,   z = 3 ,   7 ,   - 2 + r - 1 ,   - 2 ,   3

To determine

To explain:

The reason for the given lines to be parallel.

Explanation

The given two lines are,

𝓁1: x, y, z=2, 3, 4+n1, 2, -3 and

𝓁2: x, y, z=3, 7, -2+r-1, -2, 3

Definition for parallel lines.

Two lines are said to be parallel if they have no common point and they have the same direction vectors or their direction vectors are multiples of each other.

In the given two lines, there is no common point.

Consider the direction vectors

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