   Chapter 12.5, Problem 34E

Chapter
Section
Textbook Problem

# Find an equation of the plane.34. The plane through the points (3, 0, −1), (−2, −2, −    3), and (7, 1, −4)

To determine

To find: An equation of the plane that passes through the points (3,0,1) , (2,2,3) and (7,1,4) .

Explanation

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)

Write the expression to find vector from the point P(x1,y1,z1) to Q(x2,y2,z2) .

PQ=(x2x1),(y2y1),(z2z1) (2)

Consider the vector from the point (3,0,1) to (2,2,3) is (a) and the vector from the point (3,0,1) to (7,1,4) is (b) .

Calculation of vector a :

Substitute 3 for x1 , 0 for y1 , 1 for z1 , 2 for x2 , 2 for y2 , and 3 for z2 in equation (2),

a=(23),(20),[3(1)]=5,2,4

Calculation of vector b :

Substitute 0 for x1 , 1 for y1 , 1 for z1 , 1 for x2 , 1 for y2 , and 0 for z2 in equation (2),

b=(73),(10),[4(1)]=4,1,3

As both the vectors a and b lie on the plane, the cross product of a and b is the orthogonal of the plane and it is considered as normal vector

### 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

#### Convert the expressions in Exercises 8596 radical form. 34/5

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 914, evaluate the expression. 11. (3 4)2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Subtract: (18)(18)

Elementary Technical Mathematics

#### Evaluate the integral. 29. x+4x2+2x+5dx

Single Variable Calculus: Early Transcendentals

#### For f(x) = ex x, f(x) = a) ex x b) ex 1 c) e1 x d) e1 1

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

#### What is a ceiling effect, and how can it be a problem?

Research Methods for the Behavioral Sciences (MindTap Course List) 