Surfaces in Space / Vector-Valued Functions

[llauren84]

Homework Statement

Sketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function.

Homework Equations

Surfaces: z=x²+y², x+y=0
Parameter: x=t

The Attempt at a Solution

So, I sketched the space curve represented by the intersection of the two curves. It's simply a parabola. However, I can't seem to think of how to put it into a vector-valued function. I'm getting a mind block. (Perhaps, before anyone answers this, I may come up with the answer.)

 

[Dick]

Got it yet? You already have x=t. What's y in terms of t? (Put x=t into the plane equation). Finally z=?

 

[llauren84]

So, it's just z=t²+(-t)²? and..no I didn't get it yet. I put down my math and did other things. Thanks =) So, it's r(t)=<t,-t,2t²>?

 

[Dick]

Yes, that's z.