Slope of the tangent line of an intersection - Directional Derivatives

[RaoulDuke]

Homework Statement

Find the slope of the tangent line to the curve of intersection of the vertical plane x - y + 1 =0 and the surface z = x²+y² at the point (1, 2, 5)

Homework Equations

Gradients, Cross products

The Attempt at a Solution

I'm pretty lost here. I think I have to cross the two gradients of the functions that I have to find the intersection at (1, 2, 5). However, what then?

 

[lanedance]

how about finding the horizontal direction of the plane, then using it to find the directional derivative...