   Chapter 10.6, Problem 36E ### 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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# The planes x + 2 y + z = 9 and 3 x + y - 2 z = 2 intersect in a line l whose equation is x ,   y ,   z = - 1 ,   5 ,   0 + n 1 ,   - 1 ,   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+z=9 and 3x+y-2z=2 for which x=7.

Explanation

The given planes are x+2y+z=9 and 3x+y-2z=2.

The line of intersection x, y, z=-1, 5, 0+n1, -1, 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+z=9

Simplifying,

2y+z=9-7

2y+z=2

The second plane equation becomes,

37+y-2z=2

Simplifying,

21+y-2z=2

y-2z=2-21

y-2z=-19

Now, the plane equations are,

2y+z=2

y-2z=-19

We have to solve the equations to find the point 7, y, z

To determine

(b)

To find:

Find the point in the planes x+2y+z=9 and 3x+y-2z=2 for which y=16.

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