   Chapter 10.6, Problem 33E 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

For Exercises 33 and 34, apply the following theorem (stated without proof).“Two intersecting lines are perpendicular if their direction vectors v 1 = a ,   b ,   c and v 2 = d ,   e ,   f satisfy the condition that a d + b e + c f = 0 .”Are these lines perpendicular? l 1 : x ,   y ,   z = 2 ,   3 ,   4 + n 1 ,   1 ,   2 and l 2 : x ,   y ,   z = 2 ,   3 ,   4 + r - 2 ,   - 4 ,   3

To determine

To check:

Whether the given lines are perpendicular.

Explanation

The given two lines are,

𝓁1: x, y, z=2, 3, 4+n1, 1, 2 and

𝓁2: x, y, z=2, 3, 4+r-2, -4, 3

Condition for the lines to be perpendicular.

Two intersecting lines are perpendicular if their direction vectors v1=a, b, c and v2=d, e, f satisfy the condition that ad+be+cf=0.

First check whether the lines are intersecting.

Two lines are said to be intersecting if they have a common point and their direction vectors are not multiples of each other.

Here the two have common point 2, 3, 4.

They do not have same direction vectors.

Now, we have to check the condition ad+be+cf=0.

The given line equation is of the form

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