Given the vectors $v$ and $u,$ answer $a.$ through $d.$ below.

$v=11i+2j-10k,u=8i+15j$

a$.$ Find the dot product of $v$ and $u.$

$u*v=118$

Find the length of $v.$

$|v|=,($Simplify your answer. Type an exact answer, using radicals as needed.$)$