   Chapter 10.6, Problem 22E 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

Which point(s) lie in the plane 2 x + y - z = 10 ? a) 0 ,   0 ,   10 b) 5 ,   3 ,   - 3 c) 2 ,   4 ,   - 2 d) - 3 ,   6 ,   - 10

To determine

To find:

The point(s) lie in the plane 2x+y-z=10.

Explanation

Any point lying in the plane must satisfy the plane equation.

The point have coordinates such that they satisfies the plane equation.

Consider option a) 0, 0, 10

The coordinates are x=0, y=0, z=10.

Substituting the coordinates in the plane equation.

20+0-1010

0+0-1010

Hence, the point 0, 0, 6 does not lie in the plane.

Consider option b) 5, 3, -3

The coordinates are x=5, y=3, z=-3.

Substituting the coordinates in the plane equation.

25+3--310

10+3+310

1610

Hence, the point 5, 3, -3 does not lie in the plane.

Consider option c) 2, 4, -2

The coordinates are x=2, y=4, z=-2.

Substituting the coordinates in the plane equation

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