   Chapter 10.6, Problem 35E 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

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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