   Chapter 12.5, Problem 27E

Chapter
Section
Textbook Problem

# Find an equation of the plane.27. The plane through the point (1, −1, −1) and parallel to the plane 5x − y −z = 6

To determine

To find: An equation of the plane that passes through the point (1,1,1) and parallel to the plane 5xyz=6 .

Explanation

The normal vector of the plane 5xyz=6 is 5,1,1 .

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 (1,1,1) is also 5,1,1 .

n=5,1,1

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)

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