   Chapter 11.5, Problem 72E

Chapter
Section
Textbook Problem

# Parallel PlanesIn Exercises 61–64, determine whether the planes are parallel or identical. 2 x − y + 3 z = 8 8 x − 4 y + 12 z = 5

To determine
Whether the planes 2xy+3z=88x4y+12z=5

are parallel or identical.

Explanation

Given:

Equations of planes are:

2xy+3z=88x4y+12z=5

Explanation:

If normal vectors are proportional to each other the provided pair of planes will be parallel, n2=kn1

Normal vector of first plane—n1,

Normal vector of second plane —-n2

and k is any real number.

Equations of planes are:

2xy+3z=88x4y+12z=5

The coordinates of normal vector of planes will be the coefficients of x,y,z. Then,

n1=2,1,3.….

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