I have attached an image... Okay, so I have been stuck on this problem for like 2 hours now and I have no idea how to find r(x). I know the trace is the intersection of the plane and the surface. My first attempt was to substitute the plane y+2x=0 equation for the surface equation by solving for y getting y=-2x. So I got 3x^2-(-2x)^2+2x+2(-2x) = z = f(x,y). So I got an equation which is only a function of x e.g f(x) = -x^2-2x. However, how do I go from this to a vector equation r(x) so I can differentiate to get the tangent vector equation.