Tangent vector to curve of intersection of 2 surfaces

[plexus0208]

Homework Statement

Find the tangent vector at the point (1, 1, 2) to the curve of intersection of the surfaces z = x² + y² and z = x + y.

Homework Equations

The Attempt at a Solution

I haven't started the problem, because I'm not sure what the first thing to do is.
Do I have to parametrize the equations first? Then what?

 

[lanedance]

there's a couple of ways to do it... you could do it by finding a parametrisation of the curve..

an easier way woud be to notice that the tangent vector to the curve, will lie in both the tangent planes of the surfaces, then go form there

 

[plexus0208]

Oh!
If I find the gradient of each surface, and then cross the two gradients, that's it right?

 

[lanedance]

yes, as the gradients will be normal to the tangent planes, and hopefully they are not parallel...

note that only the direction of the tangent vector is required in this case