   Chapter 11.5, Problem 37E

Chapter
Section
Textbook Problem

# Finding an Equation of a PlaneIn Exercises 39–44, find an equation of the plane that passes through the given point and is perpendicular to the given vector or line.PointPerpendicular to ( 3 , 2 , 2 ) n = 2 i + 3 j − k

To determine

To calculate: Find the equation of the plane passes through the point (3,2,2) and is perpendicular to the vector n=2i+3jk.

Explanation

Given:

The plane passes through the point (3,2,2) and is perpendicular to the vector n=2i+3jk.

Formula used:

The equation of a plane in standard form is:

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

Calculation:

To determine equation of a plane:

The point through which it is passing

And the normal vector to the plane should be known.

Now since, the provided point is (3,2,2) and normal vector is, n=2i+3jk.

Now, use x1=3,y1=2 and z1=2

Point (3,2,2)

Direction numbers a=2,b=3 and c=1

Normal vector n=2i+3jk in the standard equation of the plane

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