Consider the following.

r$($t$)=(8$ t$)$i $+(5$t $4)$j $+3$t$$k$,$ P$(7,1,3)$

$($a$)$

Find the arc length function s$($t$)$ for the curve measured from the point P in the direction of increasing t$.$

s$($t$)=$

Reparametrize the curve with respect to arc length starting from P$.($Enter your answer in terms of s$.)$

r$($t$($s$))=$

$($b$)$

Find the point $7$ units along the curve $($in the direction of increasing t$)$ from P$.$

$($x$,$ y$,$ z$)=$