> 
> Let $C$ be a curve in the $(x − y)$-plane. For every point $(x, y)$ of $C$
>  let $u(x, y)$ denote the unit vector in the direction of the tangent line
>  to $C$ at $(x, y)$. Let $S$ be the surface obtained by taking the union of
>  all straight line segments connecting $(1, 2, 3)$ to points of $C$. Express
>  the area of $S$ as an **integral of the first type**, on the curve $C$, of some
>  function of $x$ and $y$. (hint: try to use the function $u(x, y)$.)
> 
> 
> 

really Hard question , i couldn't understand how to use the fact that line integral will help here since i don't have a function $f(x,y)$ to calculate $ \int\_{C} f(x(t),y(t))\sqrt{x'(t)^2 + y'(t)^2 }\ dt$ also i can parameterize $S$ like that :
$S=:k(1-x(t),2-y(t),3) , k\in[0,1]$ where $(x(t),y(t),0)$ is the curve $C$

and why $u(x,y)$ is given here.
Unit vector