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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Determine whether the points lie on a straight line.

(a) A(2, 4, 2), B(3, 7, −2), C(1, 3, 3)

(b) D(0,−5, 5), E(1, −2, 4), F(3, 4, 2)

(a)

To determine

Whether the points lie on a straight line or not.

Explanation

The points are A(2,4,2) , B(3,7,2) , and C(1,3,3) .

Consider the distance between the points A and B to be |AB| , the distance between the points B and C is |BC| , and the distance between the points A and C is |AC| .

For the three points to be on a straight line, the sum of the two shortest distances must be equal to the longest distance.

Formula:

Write the expression to find the distance between two points P1(x1,y1,z1) and P2(x2,y2,z2) .

|P1P2|=(x2x1)2+(y2y1)2+(z2z1)2 (1)

Calculation of distance between the points A and B:

In equation (1), substitute 2 for x1 , 4 for y1 , 2 for z1 , 3 for x2 , 7 for y2 , and 2 for z2 to find the distance between the points A and B.

|AB|=(32)2+(74)2+(22)2=1+9+16=26=5.0990

The distance between the points A and B is 5.0990.

Calculation of the distance between the points B and C:

In equation (1), substitute 3 for x1 , 7 for y1 , 2 for z1 , 1 for x2 , 3 for y2 , and 3 for z2 to find the distance between the points B and C

(b)

To determine

Whether the points lie on a straight line or not.

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Chapter 12 Solutions

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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

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