   Chapter 10.6, Problem 43E 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

Lines l 1 : x ,   y ,   z = 2 ,   3 ,   - 1 + n 1 ,   1 ,   2 and l 2 : x ,   y ,   z = 7 ,   7 ,   2 + r - 2 ,   - 1 ,   3 intersect at point P . Find the cvoordinates x ,   y ,   z of point P .

To determine

To explain:

Find the coordinates x, y, z of point P.

𝓁1: x, y, z=2, 3, -1+n1, 1, 2 and

𝓁2: x, y, z=7, 7, 2+r-2, -1, 3

Explanation

The given two lines are,

𝓁1: x, y, z=2, 3, -1+n1, 1, 2 and

𝓁2: x, y, z=7, 7, 2+r-2, -1, 3

It is said that the two lines are intersecting.

Write the point form of the two lines.

𝓁1=2+n, 3+n, -1+2n

𝓁2=7-2r, 7-r, 2+3r

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

2+n=7-2r

3+n=7-r

-1+2n=2+3r

From first equation, n=7-2r-2

Hence, n=5-2r

Substitute this value in second equation.

3+5-2r=7-r

Combining the like terms,

-2r+r=7-3-5

Simplifying,

-r=-1

Cancelling negative sign on both sides,

r=1

From this,

r=1

Substitute r=1 in n=5-2r

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