Answer
$(0,0,0)$ and $(1,0,1)$
Work Step by Step
Write the parametric equations for the vector equation
$r(t)= ti +(2t-t^2) k$.
We have $x=t; y=0, z=2t-t^2$
We are given that $z=x^2+y^2 \implies 2t-t^2=t^2+0^2$
and $2t-2t^2=0 \implies 2t(1-t) =0$
The points of intersection are given as:
$x=0; y=0$ and $z=2t-2t^2 = 2(0)-(0)^2=0-0=0$
and
$x=1; y=0$ and $z=2t-2t^2=2(1)-(1)^2=1$
Answer: $(0,0,0)$ and $(1,0,1)$
