   Chapter 10.6, Problem 21E 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 + 3 y + 4 z = 24 ? a) 0 ,   0 ,   6 b) 0 ,   3 ,   4 c) 4 ,   4 ,   1 d) - 2 ,   6 ,   3

To determine

To find:

The point(s) lie in the plane 2x+3y+4z=24.

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, 6

The coordinates are x=0, y=0, z=6.

Substituting the coordinates in the plane equation.

20+30+46=24

0+0+24=24

Hence, the point 0, 0, 6 lie in the plane.

Consider option b) 0, 3, 4

The coordinates are x=0, y=3, z=4.

Substituting the coordinates in the plane equation.

20+33+4424

0+9+1624

2524

Hence, the point 0, 3, 4 does not lie in the plane.

Consider option c) 4, 4, 1

The coordinates are x=4, y=4, z=1

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