( 716, #5) Find parametric equations and symmetric equations for the line passing through the points ( 2, 1, 8 ) and ( 6, 0, 3 ).

Solution:

A vector must first be calculated:

v = < 6 - 2, 0 - 1, 3 - 8 > = < 4, -1, -5 >

Either of the points can be used to find the parametric equation. Using ( 2, 1, 8 ) the parametric equations are:

x = 2 + 4t, y = 1 - t, z = 8 - 5t

Solving for t, the symmetric equations are:

by: nl