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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Give a geometric description of each family of planes.

(a) x + y + z = c

(b) x + y + cz = 1

(c) y cos θ + z sin θ = 1

(a)

To determine

To explain: The geometric description of the plane x+y+z=c.

Explanation

Given data:

Write the given plane equation as follows.

x+y+z=c

Formula used:

Write the expression to find equation of the plane through the point P0(x0,y0,z0) with normal vector n=a,b,c to the plane as follows.

a(xx0)+b(yy0)+c(zz0)=0 (1)

Write the family of planes for the equation x+y+z=c as follows.

1(x0)+1(y0)+1(zc)=0 (2)

1(x0)+1(

(b)

To determine

To explain: The geometric description of the plane x+y+cz=1.

(c)

To determine

To explain: The geometric description of the plane ycosθ+zsinθ=1.

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Chapter 12 Solutions

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