Chapter 12.1, Problem 11E

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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

Consider the distance between the points *A* and *B* to be
*B* and *C* is
*A* and *C* is

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

**Calculation of distance between the points A and B:**

In equation (1), substitute 2 for
*A* and *B*.

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
*B* and *C*

(b)

To determine

Whether the points lie on a straight line or not.

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

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P-38RECh-12 P-1PCh-12 P-2PCh-12 P-5P

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