   Chapter 11.5, Problem 49E

Chapter
Section
Textbook Problem

# Finding an Equation of a PlaneIn Exercises 45–56, find an equation of the plane with the given characteristics.The plane passes through the points ( 2 , 2 , 1 ) and ( − 1 , 1 , − 1 ) and is perpendicular to the plane 2 x − 3 y + z = 3.

To determine

To calculate: The equation of the plane passes through the points (2,2,1) and (1,1,1), and also it is perpendicular to the plane, 2x3y+z=3

Explanation

Given: The plane passes through the points (2,2,1) and (1,1,1), and also it is perpendicular to the plane, 2x3y+z=3.

Formula used: The standard equation of the plane is given by:

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.

Two choices for the point but there is no normal vector provided.

Since, the plane to be found is perpendicular to a plane whose equation is:

2x3y+z=3

This implies, the normal vector of this plane will be parallel to the required plane.

The coordinates of normal vector of the plane are the coefficients of x,y,z.

So, the normal vector to this plane is v=2,3,1.

This vector v is parallel to the required plane and the vector which extends from the point (1,1,1) to the point (2,2,1), as these points lie in the plane.

Thus, the normal vector to the required plane can be obtained by the cross product of u and v, where, u is extend from the point (1,1,1) to the point (2,2,1)

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the definite integrals in Problems 1-32.

Mathematical Applications for the Management, Life, and Social Sciences

#### Which number is the best choice for the value of a in the following graph? a) e b) 1 c) 2 d) 3

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### True or False: Du f(a, b) = ∇(a, b) · u.

Study Guide for Stewart's Multivariable Calculus, 8th 