   Chapter 11.5, Problem 71E

Chapter
Section
Textbook Problem

# Parallel PlanesIn Exercises 61–64, determine whether the planes are parallel or identical. − 5 x + 2 y − 8 z = 6 15 x − 6 y + 24 z = 17

To determine
Find if the planes 5x+2y8z=6 and 15x6y+24z=17 are parallel or identical.

Explanation

Given: Equations of planes are:

5x+2y8z=615x6y+24z=17

Explanation:

Normal vector of first plane—n1,

Normal vector of second plane —-n2

and k is any real number.

Equations of planes are:

5x+2y8z=615x6y+24z=17

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

n1=5,2,8 …… (1)

n2=15,6,24

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