   Chapter 10.6, Problem 35E ### 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
4 views

# The planes x + 2 y + 3 z = 12 and 2 x + 3 y + z = 18 intersect in the line l whose equation is x ,   y ,   z = 0 ,   6 ,   0 + n 7 ,   - 5 ,   1 . Find the point in both planes for which: a) x = 7 b) y = 16

To determine

(a)

To find:

Find the point in the planes x+2y+3z=12 and 2x+3y+z=18 for which x=7.

Explanation

The given planes are x+2y+3z=12 and 2x+3y+z=18.

The line of intersection x, y, z=0, 6, 0+n7, -5, 1.

We have to find the point in both the planes for which x=7.

Substitute x=7 in both the plane equations.

The first plane equation becomes,

7+2y+3z=12

Simplifying,

2y+3z=5

The second plane equation becomes,

27+3y+z=18

Simplifying,

14+3y+z=18

3y+z=18

To determine

(b)

To find:

Find the point in the planes x+2y+3z=12 and 2x+3y+z=18 for which y=16.

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