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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

Is the line through (−4, −6, 1) and (−2, 0, −3) parallel to the line through (10, 18,4) and (5, 3, 14)?

To determine

To find: Whether the line through the points (4,6,1) and (2,0,3) is parallel to the line through the points (10,18,4) and (5,3,14) or not.

Explanation

The condition for two lines to be in parallel, the direction vector of one of the line is multiple of the other line.

Consider the direction vector of line through the points (4,6,1) and (2,0,3) is v1 and the direction vector of line through the points (10,18,4) and (5,3,14) is v2 .

The lines to be in parallel, v2=kv1 .

Formula:

Write the expression to find direction vector of the line through the points (x1,y1,z1) and (x2,y2,z2) .

v=(x2x1),(y2y1),(z2z1) (1)

Calculation of direction vector of the line through the points (4,6,1) and (2,0,3) :

In equation (1), 4 for x1 , 6 for y1 , 1 for z1 , 2 for x2 , 0 for y2 , and 3 for z2

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Chapter 12 Solutions

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

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