   Chapter 12.5, Problem 29E

Chapter
Section
Textbook Problem

# Find an equation of the plane.29. The plane through the point (1, 1 2 , 1 3 ) and parallel to the plane x + y + z = 0

To determine

To find: An equation of the plane that passes through the point (1,12,13) and parallel to the plane x+y+z=0 .

Explanation

The normal vector of the plane x+y+z=0 is 1,1,1 .

As the two planes are in parallel, the normal vectors of both the planes are equal.

Therefore, the normal vector of the plane that passes through the point (1,12,13) is also 1,1,1 .

n=1,1,1

Formula:

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

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

Calculation of equation of the plane:

Substitute 1 for x0 , 12<

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