$11.$If $\frac{?}{\text{b}\text{a}\text{r}}(f)(t)=e^{t}cos\frac{t}{b}ar()+e^{t}sin\frac{t}{b}ar()+4\frac{e^t}{b}ar(k),$ and

$\frac{?}{\text{b}\text{a}\text{r}}(k),$ answer each of the following:

$($i$)$ Show that the curve $\frac{?}{\text{b}\text{a}\text{r}}(f)(t)$ lies on the upper half of the cone

$z^2=16(x^2+y^2).$

$($ii$)$ Show that the curves $\frac{?}{\text{b}\text{a}\text{r}}(f)(t)\frac{\text{\&}}{b}ar(g)(t)$ intersect at the point $(1,0,4)$ and find the angle of intersection at this point.

$($iii$)$ Find an equation of the osculating plane to the curve $\frac{?}{\text{b}\text{a}\text{r}}(f)(t)$ at $t=0.$

$($iv$)$ Find the curvature of the curve $\frac{?}{\text{b}\text{a}\text{r}}(f)(t).$

$($v$)$ Find the components of the acceleration of a particle moving along $\frac{?}{\text{b}\text{a}\text{r}}(f)(t)$ along the unit tangent vector and along the principal normal vector.