Question $3$: In computer graphics objects seen by the eye in space need to be represented as images on a two$-$dimensional plane. Suppose that the eye is at $E(x_0,0,0)$ and that we want to represent a point $P_1(x_1,y_1,z_1)$ as a point on the $yz-$plane. To do this, we project $P_1$ onto the plane with a ray from $E.$ The point $P_1$ will be portrayed as the point $P(0,y,z).$ Our task is to find $y$ and $z$ in terms of $x_0,x_1,y_1,$ and $z_1.$

a$)$ Write a vector equation that holds between vec$(EP)$ and vec$(E{P}_1).$ Use the equation to express $y$ and $z$ in terms of $x_0,x_1,y_1,$ and $z_1.$

b$)$ Test the formulas obtained for $y$ and $z$ by investigating their behavior:

i$)$ at $x_1=0$;

ii$)$ at $x_1=x_0$;

iii$)$ and as $x_0.$