Q$\mathrm{.}23$ Let $u=($:$7,-4$:$)$ and $v=($:$-2,8$:$).$ Find the $($a$)$ component form and $($b$)$ magnitude $($length$)$ of the vector.

$\frac{5}{13}u+\frac{12}{13}v$

a$.\frac{5}{13}u+\frac{12}{13}v=$

$($Type integers or simplified fractions.$)$

b$.$ The magnitude of the vector is $$

$($Type an exact answer, using radicals as needed.$)$