(Solved): 5) Find parametric equations that describe the intersection of the cone \( z=x^{2}+y^{2} \) and the ...

5) Find parametric equations that describe the intersection of the cone \( z=x^{2}+y^{2} \) and the plane \( x= \) \( 2 z \) 6) Determine if the curves described by the parametric equations below intersect. If they intersect determine the point(s) of intersection. Also determine if particles described by the parametric equations collide. \[ \begin{array}{l} \vec{r}_{1}(t)=\left\langle t, t^{2}, t^{3}\right\rangle \\ \vec{r}_{2}(t)=\langle 1+2 t, 1+6 t, 1+14 t\rangle \end{array} \]