4. (15 points) Let $f(x,y)$ be a differentiable function with continuous partial derivatives with $f(1,2) = 3$, $f_x(1,2) = 1$, $f_y(1,2) = -2$. Assume that $C$ is a curve given as the intersection of the plane $x = 1$ and the surface $z = f(x,y)$. If $r(t)$ is a parametric vector equation of the line that is on the plane $x = 1$ and tangent to $C$ at the point $(1,2,3)$, then reparametrize $r(t)$ with respect to arc length measured from $(1,2,3)$ in the direction of increasing $t$.
