Consider the curve $C$ described $by$ the position vector function vec$(r)(t)=($:$t,-t^2,3$:$)$ for $-3t3$

and the point $PonC$ which corresponds $tot=2.$

$(i)$ Sketch the curve $Cinanxyz-$coordinate system. Indicate the orientation $of$ the curve and

locate the point $Pon$ the curve.

$(ii)$ Determine vec$(r)(2)$ and vec$(r{)}^{\text{'}}(2)$ and sketch these vectors $in$ the appropriate locations $in$ you answer

$to$ part $(i)$

$(iii)$ Determine vec$(T)(2)$

$(iv)$ Determine vec$(N)vec(N)$ geometricallyC $at$ the point $P.$

$(vi)$ Determine the radius and center $of$ the circle $of$ curvature for the point $PonC.$