   Chapter 11, Problem 47RE

Chapter
Section
Textbook Problem

# Finding an Equation of a PlaneIn Exercises 41–44, find an equation of the plane with the given characteristics.The plane passes through ( − 3 , − 4 , 2 ) ,   ( − 3 , 4 , 1 ) , and ( 1 , 1 , − 2 ) .

To determine

To calculate: For The plane passes through the points (3,4,2), (3,4,1) and (1,12) The equation of a plane.

Explanation

Given:

The plane passes through the points (3,4,2), (3,4,1) and (1,12).

Formula used:

The plane containing the point a,b,c and having normal vector n=a,b,c can be shown by the equation of plane:

a(xx1)+b(yy1)+c(zz1)=0

Which can be written in general form as: ax+by+cz+d=0.

Calculation:

Find a point in the plane and a vector that is normal to the plane:

Asthere is not a normal vector.

v=(1(3)),(1(4)),(22)=4,5,4

And

u=(3(3)),(4(4)),(12)=0,8,1

Cross product of vectors u and v to obtain normal vector:

n<

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