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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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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.

2 x z = 1 , 4 x + y + 8 z = 10

To determine

Weather the given planes 2xz=1 and 4x+y+8z=10 are parallel,

perpendicular or neither parallel nor perpendicular.

Explanation

Given Information:

The equations of planes are:

2xz=14x+y+8z=10

Consider the provided equations:

2xz=1 and 4x+y+8z=10

The standard equations of planes are a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d=20

Planes to be parallel

a1a2=b1b2=c1c2=k …… (1)

Planes to be perpendicular

a1a2+b1b2+c1c2=0 …… (2)

Equation of planes

2xz=1 …… (3)

And

4x+y+8z=10 …… (4)

Now, on comparing equation (3) with standard equation of plane a1x+b1y+c1z+d1=0:

a1=2

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