# Thread: Parametric Equation for a Line

1. ## Parametric Equation for a Line

Find parametric equations for the line through the point, that is parallel to the given plane, and perpendicular to the following line.

Given information:
(0,1,2)
x + y + z = 4
x = 1 + t, y = 1 - t, z = 2t
x = 3s

Need to find:
y = ?
z = ?

Attempt:
x = 3s = 1 + t
t = 3s - 1

y = 1 (3s -1) = 2 - 3s
z = 2 (3s -1) = 6s -1

Not sure where I went wrong, or if I even did this correctly. Thanks in advance for any help or suggestions.

2. The direction vector of the line is $<1,1,1>\times<1,-1,2>$.