menu
bartleby
search
close search
Hit Return to see all results
Subscribe
Sign in
Subjects
Business
Accounting
Economics
Finance
Leadership
Management
Marketing
Operations Management
Engineering
Bioengineering
Chemical Engineering
Civil Engineering
Computer Engineering
Computer Science
Electrical Engineering
Mechanical Engineering
Math
Advanced Math
Algebra
Calculus
Geometry
Probability
Statistics
Trigonometry
Science
Advanced Physics
Biochemistry
Biology
Chemistry
Earth Science
Health & Nutrition
Nursing
Physics
Social Science
Anthropology
Psychology
Sociology

Math
CalculusMultivariable Calculus8th Edition

close solutoin list
Chapter 12.5, Problem 70E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
Problem 83E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Use the formula in Exercise 12.4.45 to find the distance from the point to the given line.

(0, 1, 3); x = 2t, y = 6 − 2t, z = 3 + t

To determine

To find: The distance from the point (0, 1, 3) to the line x=2t, y=6−2t, z=3+t .

Explanation

Consider the line L passes through the points Q and R .

Consider a point P(x0, y0, z0)=(0, 1, 3) which is not on the line L .

Formula:

Write the expression to find the distance from the point P(x0, y0, z0) to the line L .

d=|a×b||a| (1)

Here,

a is the direction vector from the point Q to the point R and

b is the direction vector from the point Q to the point P(x0, y0, z0) .

The points Q and R are determined by varying the scalar parameter t in the line equation.

Write the symmetric equations of the line as follows.

x=2t, y=6−2t, z=3+t (2)

Consider the value of scalar parameter t as 0 and obtain the point Q .

Substitute 0 for t in equation (2) to obtain the point Q .

x=2(0), y=6−2(0), z=3+0x=0, y=6, z=3

The point Q on the line is (0, 6, 3) .

Consider the value of scalar parameter t as 1 and obtain the point R .

Substitute 1 for t in equation (2) to obtain the point R .

x=2(1), y=6−2(1), z=3+1x=2, y=4, z=4

The point R on the line is (2, 4, 4) .

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

PQ→=〈(x2−x1), (y2−y1), (z2−z1)〉 (3)

Calculation of direction vector a(QR→) :

Substitute 0 for x1 , 6 for y1 , 3 for z1 , 2 for x2 , 4 for y2 , and 4 for z2 in equation (3),

a=〈(2−0), (4−6), (4−3)〉=〈2, −2, 1〉=2i−2j+k

Calculation of direction vector b(QP→) :

Substitute 0 for x1 , 6 for y1 , 3 for z1 , 0 for x2 , 1 for y2 , and 3 for z2 in equation (3),

b=〈(0−0), (1−6), (3−3)〉=〈0, −5, 0〉

Write the expression to find cross product of direction vectors

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution
arrow_back
Chapter 12.5,
Problem 69E
Chapter 12.5,
Problem 71E
arrow_forward

The Solution to Your Study Problems

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

Get Started

Chapter 12 Solutions

Show all chapter solutions add
Sect-12.1 P-1ESect-12.1 P-2ESect-12.1 P-3ESect-12.1 P-4ESect-12.1 P-5ESect-12.1 P-6ESect-12.1 P-7ESect-12.1 P-8ESect-12.1 P-9ESect-12.1 P-10E
Sect-12.1 P-11ESect-12.1 P-12ESect-12.1 P-13ESect-12.1 P-14ESect-12.1 P-15ESect-12.1 P-16ESect-12.1 P-17ESect-12.1 P-18ESect-12.1 P-19ESect-12.1 P-20ESect-12.1 P-21ESect-12.1 P-22ESect-12.1 P-23ESect-12.1 P-24ESect-12.1 P-25ESect-12.1 P-26ESect-12.1 P-27ESect-12.1 P-28ESect-12.1 P-29ESect-12.1 P-30ESect-12.1 P-31ESect-12.1 P-32ESect-12.1 P-33ESect-12.1 P-34ESect-12.1 P-35ESect-12.1 P-36ESect-12.1 P-37ESect-12.1 P-38ESect-12.1 P-39ESect-12.1 P-40ESect-12.1 P-41ESect-12.1 P-42ESect-12.1 P-43ESect-12.1 P-44ESect-12.1 P-45ESect-12.1 P-46ESect-12.1 P-47ESect-12.1 P-48ESect-12.2 P-1ESect-12.2 P-2ESect-12.2 P-3ESect-12.2 P-4ESect-12.2 P-5ESect-12.2 P-6ESect-12.2 P-7ESect-12.2 P-8ESect-12.2 P-9ESect-12.2 P-10ESect-12.2 P-11ESect-12.2 P-12ESect-12.2 P-13ESect-12.2 P-14ESect-12.2 P-15ESect-12.2 P-16ESect-12.2 P-17ESect-12.2 P-18ESect-12.2 P-19ESect-12.2 P-20ESect-12.2 P-21ESect-12.2 P-22ESect-12.2 P-23ESect-12.2 P-24ESect-12.2 P-25ESect-12.2 P-26ESect-12.2 P-27ESect-12.2 P-28ESect-12.2 P-29ESect-12.2 P-30ESect-12.2 P-31ESect-12.2 P-32ESect-12.2 P-33ESect-12.2 P-34ESect-12.2 P-35ESect-12.2 P-36ESect-12.2 P-37ESect-12.2 P-38ESect-12.2 P-39ESect-12.2 P-40ESect-12.2 P-41ESect-12.2 P-42ESect-12.2 P-43ESect-12.2 P-44ESect-12.2 P-45ESect-12.2 P-46ESect-12.2 P-47ESect-12.2 P-48ESect-12.2 P-49ESect-12.2 P-50ESect-12.2 P-51ESect-12.2 P-52ESect-12.3 P-1ESect-12.3 P-2ESect-12.3 P-3ESect-12.3 P-4ESect-12.3 P-5ESect-12.3 P-6ESect-12.3 P-7ESect-12.3 P-8ESect-12.3 P-9ESect-12.3 P-10ESect-12.3 P-11ESect-12.3 P-12ESect-12.3 P-13ESect-12.3 P-14ESect-12.3 P-15ESect-12.3 P-16ESect-12.3 P-17ESect-12.3 P-18ESect-12.3 P-19ESect-12.3 P-20ESect-12.3 P-21ESect-12.3 P-22ESect-12.3 P-23ESect-12.3 P-24ESect-12.3 P-25ESect-12.3 P-26ESect-12.3 P-27ESect-12.3 P-28ESect-12.3 P-29ESect-12.3 P-30ESect-12.3 P-31ESect-12.3 P-32ESect-12.3 P-33ESect-12.3 P-34ESect-12.3 P-35ESect-12.3 P-36ESect-12.3 P-37ESect-12.3 P-38ESect-12.3 P-39ESect-12.3 P-40ESect-12.3 P-41ESect-12.3 P-42ESect-12.3 P-43ESect-12.3 P-44ESect-12.3 P-45ESect-12.3 P-46ESect-12.3 P-47ESect-12.3 P-48ESect-12.3 P-49ESect-12.3 P-50ESect-12.3 P-51ESect-12.3 P-52ESect-12.3 P-53ESect-12.3 P-54ESect-12.3 P-55ESect-12.3 P-56ESect-12.3 P-57ESect-12.3 P-58ESect-12.3 P-59ESect-12.3 P-60ESect-12.3 P-61ESect-12.3 P-62ESect-12.3 P-63ESect-12.3 P-64ESect-12.3 P-65ESect-12.4 P-1ESect-12.4 P-2ESect-12.4 P-3ESect-12.4 P-4ESect-12.4 P-5ESect-12.4 P-6ESect-12.4 P-7ESect-12.4 P-8ESect-12.4 P-9ESect-12.4 P-10ESect-12.4 P-11ESect-12.4 P-12ESect-12.4 P-13ESect-12.4 P-14ESect-12.4 P-15ESect-12.4 P-16ESect-12.4 P-17ESect-12.4 P-18ESect-12.4 P-19ESect-12.4 P-20ESect-12.4 P-21ESect-12.4 P-22ESect-12.4 P-23ESect-12.4 P-24ESect-12.4 P-25ESect-12.4 P-26ESect-12.4 P-27ESect-12.4 P-28ESect-12.4 P-29ESect-12.4 P-30ESect-12.4 P-31ESect-12.4 P-32ESect-12.4 P-33ESect-12.4 P-34ESect-12.4 P-35ESect-12.4 P-36ESect-12.4 P-37ESect-12.4 P-38ESect-12.4 P-39ESect-12.4 P-40ESect-12.4 P-41ESect-12.4 P-42ESect-12.4 P-43ESect-12.4 P-44ESect-12.4 P-45ESect-12.4 P-47ESect-12.4 P-48ESect-12.4 P-49ESect-12.4 P-50ESect-12.4 P-51ESect-12.4 P-52ESect-12.4 P-53ESect-12.4 P-54ESect-12.5 P-1ESect-12.5 P-2ESect-12.5 P-3ESect-12.5 P-4ESect-12.5 P-5ESect-12.5 P-6ESect-12.5 P-7ESect-12.5 P-8ESect-12.5 P-9ESect-12.5 P-10ESect-12.5 P-11ESect-12.5 P-12ESect-12.5 P-13ESect-12.5 P-14ESect-12.5 P-15ESect-12.5 P-16ESect-12.5 P-17ESect-12.5 P-18ESect-12.5 P-19ESect-12.5 P-20ESect-12.5 P-21ESect-12.5 P-22ESect-12.5 P-23ESect-12.5 P-24ESect-12.5 P-25ESect-12.5 P-26ESect-12.5 P-27ESect-12.5 P-28ESect-12.5 P-29ESect-12.5 P-30ESect-12.5 P-31ESect-12.5 P-32ESect-12.5 P-33ESect-12.5 P-34ESect-12.5 P-35ESect-12.5 P-36ESect-12.5 P-37ESect-12.5 P-38ESect-12.5 P-39ESect-12.5 P-40ESect-12.5 P-41ESect-12.5 P-42ESect-12.5 P-43ESect-12.5 P-44ESect-12.5 P-45ESect-12.5 P-46ESect-12.5 P-47ESect-12.5 P-48ESect-12.5 P-49ESect-12.5 P-50ESect-12.5 P-51ESect-12.5 P-52ESect-12.5 P-53ESect-12.5 P-54ESect-12.5 P-55ESect-12.5 P-56ESect-12.5 P-57ESect-12.5 P-58ESect-12.5 P-59ESect-12.5 P-60ESect-12.5 P-61ESect-12.5 P-62ESect-12.5 P-63ESect-12.5 P-64ESect-12.5 P-65ESect-12.5 P-66ESect-12.5 P-67ESect-12.5 P-68ESect-12.5 P-69ESect-12.5 P-70ESect-12.5 P-71ESect-12.5 P-72ESect-12.5 P-73ESect-12.5 P-74ESect-12.5 P-75ESect-12.5 P-76ESect-12.5 P-77ESect-12.5 P-78ESect-12.5 P-79ESect-12.5 P-80ESect-12.5 P-81ESect-12.5 P-82ESect-12.5 P-83ESect-12.6 P-1ESect-12.6 P-2ESect-12.6 P-3ESect-12.6 P-4ESect-12.6 P-5ESect-12.6 P-6ESect-12.6 P-7ESect-12.6 P-8ESect-12.6 P-9ESect-12.6 P-10ESect-12.6 P-11ESect-12.6 P-12ESect-12.6 P-13ESect-12.6 P-14ESect-12.6 P-15ESect-12.6 P-16ESect-12.6 P-17ESect-12.6 P-18ESect-12.6 P-19ESect-12.6 P-20ESect-12.6 P-21ESect-12.6 P-22ESect-12.6 P-23ESect-12.6 P-24ESect-12.6 P-25ESect-12.6 P-26ESect-12.6 P-27ESect-12.6 P-28ESect-12.6 P-29ESect-12.6 P-30ESect-12.6 P-31ESect-12.6 P-32ESect-12.6 P-33ESect-12.6 P-34ESect-12.6 P-35ESect-12.6 P-36ESect-12.6 P-37ESect-12.6 P-38ESect-12.6 P-43ESect-12.6 P-44ESect-12.6 P-45ESect-12.6 P-46ESect-12.6 P-47ESect-12.6 P-48ESect-12.6 P-49ESect-12.6 P-50ESect-12.6 P-51ESect-12.6 P-52ECh-12 P-1RCCCh-12 P-2RCCCh-12 P-3RCCCh-12 P-4RCCCh-12 P-5RCCCh-12 P-6RCCCh-12 P-7RCCCh-12 P-8RCCCh-12 P-9RCCCh-12 P-10RCCCh-12 P-11RCCCh-12 P-12RCCCh-12 P-13RCCCh-12 P-14RCCCh-12 P-15RCCCh-12 P-16RCCCh-12 P-17RCCCh-12 P-18RCCCh-12 P-19RCCCh-12 P-1RQCh-12 P-2RQCh-12 P-3RQCh-12 P-4RQCh-12 P-5RQCh-12 P-6RQCh-12 P-7RQCh-12 P-8RQCh-12 P-9RQCh-12 P-10RQCh-12 P-11RQCh-12 P-12RQCh-12 P-13RQCh-12 P-14RQCh-12 P-15RQCh-12 P-16RQCh-12 P-17RQCh-12 P-18RQCh-12 P-19RQCh-12 P-20RQCh-12 P-21RQCh-12 P-22RQCh-12 P-1RECh-12 P-2RECh-12 P-3RECh-12 P-4RECh-12 P-5RECh-12 P-6RECh-12 P-7RECh-12 P-8RECh-12 P-9RECh-12 P-10RECh-12 P-11RECh-12 P-12RECh-12 P-13RECh-12 P-14RECh-12 P-15RECh-12 P-16RECh-12 P-17RECh-12 P-18RECh-12 P-19RECh-12 P-20RECh-12 P-21RECh-12 P-22RECh-12 P-23RECh-12 P-24RECh-12 P-25RECh-12 P-26RECh-12 P-27RECh-12 P-28RECh-12 P-29RECh-12 P-30RECh-12 P-31RECh-12 P-32RECh-12 P-33RECh-12 P-34RECh-12 P-35RECh-12 P-36RECh-12 P-37RECh-12 P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

Convert the expressions in Exercises 31-36 to positive exponent form. 45y3/4

Finite Mathematics and Applied Calculus (MindTap Course List)

Finding a Limit In Exercises 11-28, find the limit. limx44x1

Calculus: Early Transcendental Functions

If p is a polynomial, Show that limxa p(x) = p(a)

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 25 and 26, find the line that best fits the given points, and compute the correlation coefficient....

Applied Calculus

Orbit of a Satellite A satellite is in orbit around the moon. A coordinate plane containing the orbit is set up...

Precalculus: Mathematics for Calculus (Standalone Book)

Let T and N be the tangent and normal lines to the ellipse x2/9 + y2/4 = 1 at any point P on the ellipse in the...

Calculus: Early Transcendentals

Checkpoint 1 Worked-out solution availlable at LarsonAppliedCalculus.com Find the derivative of each function. ...

Calculus: An Applied Approach (MindTap Course List)

Draw a histogram for the distribution of scores shown in the following table. x f 10 2 9 4 8 1 7 1 6 4 5 2

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

SOC On the scale mentioned in problem 5.7, if a score of 40 or more is considered highly prejudiced. what is th...

Essentials Of Statistics

If A, B, and C are the vertices of a triangle, find AB+BC+CA

Calculus (MindTap Course List)

A sample is selected from a population with a mean of =40 and a standard deviation of =8 . If the sample has n=...

Statistics for The Behavioral Sciences (MindTap Course List)

Explain what it means to say that limx1f(x)=3andlimx1+f(x)=7 In this situation is it possible that limx1 f(x) e...

Single Variable Calculus

Small Breweries U.S. craft-beer breweries (breweries that make fewer than 6 million barrels annually and are le...

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

In Exercises 2330, factor each expression and simplify as much as possible. (x+1)3+(x+1)5

Finite Mathematics

In each of the following problems, the binomial distribution will be used. Answers may vary slightly depending ...

Understanding Basic Statistics

A company uses three different assembly linesA1, A2, and A3to manufacture a particular component. Of those manu...

Probability and Statistics for Engineering and the Sciences

Determine the distance a ball rolls, on inclined plane2, during each of the following time intervals. a. 1st se...

Mathematical Excursions (MindTap Course List)

In Problems 22-24, a supply function and a demand function are given. (a) Sketch the first-quadrant portions of...

Mathematical Applications for the Management, Life, and Social Sciences

Simplify the algebraic expressions in Problems 15-34 by removing parentheses and combining similar terms. Objec...

Intermediate Algebra

Les Roberts, a self-employed commercial artist, had total net earnings of $60,000 last year. What was the amoun...

Contemporary Mathematics for Business & Consumers

Solve each equation by factoring: 5x26x=0

Elementary Technical Mathematics

Points A and B have symmetry with respect to a vertical line x=a or a horizontal line y=b. Give an equation, su...

Elementary Geometry For College Students, 7e

Use Simpsons Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x...

Single Variable Calculus: Early Transcendentals

Determining Convergence or Divergence In Exercises 11-18, determine the convergence or divergence of the sequen...

Calculus of a Single Variable

Evaluate the iterated integral: 010x1x2dydx

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises , prove the statements concerning the relation on the set of all integers. 17. If and , then .

Elements Of Modern Algebra

Multiply. (2cos+3)(4cos5)

Trigonometry (MindTap Course List)

What is the number of the integral formula in your texts Table of Integrals that may be used to evaluate x2+2x+...

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

The scalar projection of on is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercise 15-24, compute the steady-state matrix of each stochastic matrix. [10.2.101.4.2000.400.4.3]

Finite Mathematics for the Managerial, Life, and Social Sciences

Construct an equilateral triangle and its three altitudes. What does intuition tell you about the three medians...

Elementary Geometry for College Students

Finding Partial Derivative ImplicitlyIn Exercises 55 and 56, differentiate implicitly to find the first partial...

Calculus

Parallel Vectors In Exercises 63-66, determine which of the vectors is/are parallel to z. Use a graphing utilit...

Multivariable Calculus

Finding a Limit In Exercises 71-76, find each limit. (a) limx0f(x+x,y)f(x,y)x (b) limy0f(x,y+y)f(x,y)y f(x,y)=1...

Calculus (MindTap Course List)

Over the past few years the percentage of students who leave Lakeland College at the end of the first year has ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Let A = a, e, i, B = c, d, e, and V = a, e, i, o, u. Self Check a. Is BV? b. Find BV c. Find AV

College Algebra (MindTap Course List)

Explain how holding a participant variable such as gender constant prevents the variable from becoming a confou...

Research Methods for the Behavioral Sciences (MindTap Course List)

College student attitudes about e-books were investigated in a survey of 1625 students. Students were asked to ...

Introduction To Statistics And Data Analysis

Explain the general advantages and disadvantages of between-subjects design compared to within-subjects design.

Research Methods for the Behavioral Sciences (MindTap Course List)

Express the following decimal numbers as hexadecimal numbers. 65 328

Mathematics For Machine Technology

A university found that 20% of its students withdraw without completing the introductorystatistics course. Assu...

Statistics for Business & Economics, Revised (MindTap Course List)

bartleby
© bartleby 2019