# Trajectory as an intersection of two surfaces

• September 27th 2010, 02:10 PM
Ulysses
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.
• September 27th 2010, 05:18 PM
Ackbeet
In looking at your trajectory there, can you come up with any relationships between the different components of your vector?
• September 27th 2010, 05:53 PM
Ulysses
I've solved it.
x=t²
y=2t -> x=z
z=t²
y²=4t²=4x
y²=4x

And thats it :p
• September 28th 2010, 01:21 AM
Ackbeet
Looks good. Glad you got it.