   Chapter 11.5, Problem 33E

Chapter
Section
Textbook Problem

# Checking Points in a Plane In Exercises 37 and 38, determine whether each point lies in the plane. x + 2 y − 4 z − 1 = 0 (a) ( − 7 , 2 , − 1 ) (b) ( 5 , 2 , 2 ) (c) ( − 6 , 1 , − 1 )

(a)

To determine
Find if the provided point (7,2,1) lies in the plane x+2y4z1=0.

Explanation

Given:

The equation of the plane is x+2y4z1=0 and the provided point is (7,2,1).

Explanation:

In order to check whether the provided point lies in the plane or not:

It should satisfy the provided point in the equation of a plane.

The equation of the plane is,

x+2y4z1=0

point is (7,2,1).

Further on substituting x=7,y=2 and z=1 in the equation of plane

(b)

To determine
Find if the provided point (5,2,2) lies in the plane x+2y4z1=0.

(c)

To determine
Find if the provided point (6,1,1) lies in the plane x+2y4z1=0.

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