(716, #13) (a) Find symmetric equations for the line that passes through the point ( 0, 2, -1 ) and is parallel to the line with parametric equations x = 1+ 2t, y = 3t, and z=5-7t.
(b) Find the points in which the required line in part (a) intersects the coordinate planes.

Solution:

(a) The parametric equations for the parallel line through the point ( 0, 2, -1) would be :

x = 0 + 2t, y = 2 + 3t, z = -1 -7t

Solving for t, the symmetric equations are:

(b) The xy-plane intercept is where z = 0. Thus:

The yz-plane intercept is where x = 0. Thus:

The xz-plane intercept is where y = 0. Thus :

The line intersects the coordinate planes at the points

by: nl