   Chapter 12.5, Problem 8E

Chapter
Section
Textbook Problem

# Find parametric equations and symmetric equations for the line.8. The line through the points (1, 2.4, 4.6) and (2.6, 1.2, 0.3)

To determine

To find: The parametric equations and the symmetric equations for the line through the points (1,2.4,4.6) and (2.6,1.2,0.3).

Explanation

Formula used:

The expressions to find the parametric equations for a line through the point (x0,y0,z0) and parallel to the direction vector a,b,c.

x=x0+at,y=y0+bt,z=z0+ct (1)

The expression to find direction vector (v) for the line through the points P0(x0,y0,z0) and P1(x1,y1,z1).

a,b,c=(x1x0),(y1y0),(z1z0) (2)

The expressions to find the symmetric equations for a line through the point (x0,y0,z0) and parallel to the direction vector a,b,c.

xx0a=yy0b=zz0c (3)

Calculation:

Calculation of direction vector (v):

Consider the points P0 (1,2.4,4.6) and P1 is (2.6,1.2,0.3).

In equation (2), substitute 1 for x0, 2.4 for y0, 4.6 for z0, 2.6 for x1, 1.2 for y1, and 0.3 for z1.

a,b,c=(2

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