# Thread: Euclidean spaces - nonparametric equation of a plane

1. ## Euclidean spaces - nonparametric equation of a plane

I'm trying to study Euclidean spaces and one of the exercises is to derive the nonparametric equation for the following plane:
x = 2 - 3s + t
y = 4
z = 1 + s + t
I tried to write a new equation expressed in terms of x and y only:-
t = x - 2 + 3s = z -1 - s
However, I was stuck because I couldn't solve for s and t.
The textbook lists answer y=4 as the answer. Why? Please help me understand! Thank you!

2. Originally Posted by math beginner
I'm trying to study Euclidean spaces and one of the exercises is to derive the nonparametric equation for the following plane:
x = 2 - 3s + t
y = 4
z = 1 + s + t
I tried to write a new equation expressed in terms of x and y only:-
t = x - 2 + 3s = z -1 - s
However, I was stuck because I couldn't solve for s and t.
The textbook lists answer y=4 as the answer. Why? Please help me understand! Thank you!
Eliminate the variables s and t in the system of simultaneous equations:

[1]: x = 2 - 3s + t
[2]: y = 4 + 0s + 0t
[3]: z = 1 + s + t

Calculate s and t using [1] and [3] and plug the results into [2]

If you now feel as if someone has made a practical joke you can use the cross-product of $(-3, 0, 1) \times (1, 0, 1)=(0,4,0)$ to determine the equation of the plane.