Consider the curve described $by$ the following vector function.

$r(t)=(70e^{-t}cost)i+(70e^{-t}sint)j+(7-7e^{-t})k,$ for $t0$

$a.$ What $is$ the initial point $of$ the path corresponding $tor(0)?$

$b.$ What $is\underset{t}{lim}r(t)?$

$c.$ Eliminate the parameter $tto$ show that the curve $r(t)$ lies $on$ the surface $z=7-\frac{r}{10},$ where $r^2=x^2+y^2.$

$a.$ The initial point $of$ the path corresponding $tor(0)is$

$.$

$(Simplify$ your answer. Type integers $or$ decimals.$)$