Find a set of parametric equations for the tangent line to the curve of intersection of the surface at the given point

Question

The given is $$z=\sqrt{x^2+y^2}$$ $$3x-5y+7z=24$$ $$(3,4,5)$$ First we find the gradient of first equation which we'll call $F_{(x,y,z)}$ $$F_{(x,y,z)}= \sqrt{x^2+y^2}-z$$ $$F_{(x,y,z)}= \left<\frac{x}{\sqrt{x^2+y^2}},\frac{y}{\sqrt{x^2+y^2}},-1 \right>$$ Now. for the second which we'll call $G_{x,y,z}$ $$G_{x,y,z}=\left<3,-5,7 \right>$$ Now we take the cross product of the two vectors which is: $$\left<\frac{3}{5}, \frac{-36}{5}, \frac{-27}{5} \right>$$ Now if we multiply the cross product by $\frac{5}{3}$ we get $$\left<1,-12,-9\right>$$ So our parametric equations are: $$\frac{x-3}{1} ,\frac{y-4}{-12}, \frac{z-5}{-9}$$ I have checked all my work and I'm 99.9% sure I have it all right but the website we are using for turning in our homework says it is wrong.