   Chapter 10.6, Problem 44E ### 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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# Lines l 1 : x ,   y ,   z = 2 ,   0 ,   3 + n 2 ,   - 3 ,   5 and l 2 : x ,   y ,   z = 4 ,   1 ,   - 4 + r - 1 ,   2 ,   - 4 intersect at point P . Find the coordinates x ,   y ,   z of point P .

To determine

To find:

The coordinates x, y, z of point P.

𝓁1: x, y, z=2, 0, 3+n2, -3, 5 and

𝓁2: x, y, z=4, 1, -4+r-1, 2, -4

Explanation

The given two lines are,

𝓁1: x, y, z=2, 0, 3+n2, -3, 5 and

𝓁2: x, y, z=4, 1, -4+r-1, 2, -4

It is said that the two lines are intersecting.

Write the point form of the two lines.

𝓁1=2+2n, 0-3n, 3+5n

𝓁2=4-r, 1+2r, -4-4r

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

2+2n=4-r

-3n=1+2r

3+5n=-4-4r

From first equation, r=4-2-2n

Hence, r=2-2n

Substitute this value in second equation.

-3n=1+22-2n

Multiplying,

-3n=1+4-4n

Combining the like terms,

-3n+4n=1+4

Simplifying,

n=5

From this,

n=5

Substitute n=5 in r=2-2n

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