# Thread: Trajectory as an intersection of two surfaces

1. ## Trajectory as an intersection of two surfaces

Well, I must express this trajectory: $\vec{r}=(t^2,2t,t^2)$ as an intersection of two surfaces. I really don't know how to work this. It seems to be some kind of parabola, I've tried to figure it out how it would look, and I get how it would look on the planes xy and xz, but I'd really like to see some step by step for solving this. I couldn't get anywhere yet.

Bye, and thanks off course.

2. In looking at your trajectory there, can you come up with any relationships between the different components of your vector?

3. I've solved it.
x=t²
y=2t -> x=z
z=t²
y²=4t²=4x
y²=4x

And thats it

4. Looks good. Glad you got it.