   Chapter 7.2, Problem 21E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Comparing Planes In Exercises 13–22, determine whether the planes a 1 x + b 1 y + c 1 z = d 1 and a 2 x + b 2 y + c 2 z = d 2 are parallel, perpendicular, or neither. The planes are parallel when there exists a nonzero constant k such that a 1 = k a 2 ,     b 1 = k b 2 , and c 1 = k c 2 , and are perpendicular when a 1 a 2 + b 1 b 2 + c 1 c 2 = 0. x = 3 ,     z = − 1

To determine

Weather the equations of planes x=3and z=1, are parallel, perpendicular or not parallel, not perpendicular.

Explanation

Given Information:

Equations of given planes are x=3and z=1.

Consider the provided equations:

x=3and z=1

If a1x+b1y+c1z=d1 and a2x+b2y+c2z=d2 are two planes.

Planes are parallel if

a2a1=b2b1=c2c1=k(constant)

Planes are perpendicular if

a1a2+b1b2+c1c2=0

Equations of given planes are

x=3

And

z=1

Now, on comparing the equations x=3  with a1x+b1y+c1y=d1:

a1=1b1=0c1=0d1=3

And, on comparing t

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