( 716, #9) Find parametric equations and symmetric equations for the line passing through the points
( -1/3, 1, 1 ) and ( 0, 5, -8 ).

Solution:

A vector must be calculated first:

v = < 0 - ( -1/3), 5 - 1, -8 - 1 > = < 1/3, 4, -9 >

Either of the points can be used to find the parametric equations. Using the point ( -1/3, 1, 1 ) the parametric equations are:

x = -1/3 + t/3, y = 1 + 4t, z = 1 - 9t

Solving for t, the symmetric equations are:

by: nl