Intersection of surfaces/tangent vector

[Odyssey]

Hi, how do I find a tangent vector to the curve intersection of the surfaces 2x^2+2y^2-z^2=25 and x^2+y^2=z^2 which has positive x-direction?

Thanks in advance.

[arildno]

Note that your last equation implies that we may write:
x=z\cos\theta,y=z\sin\theta,0\leq\theta\leq2\pi
Inserting these relations into your first equation, yields:
z^{2}=\frac{25}{3}
Can you take it from here?