Answer
$\sqrt{38}+\sqrt{17}$.
Work Step by Step
We know that if $v=ai+bj+ck$ and $w=di+ej+fk$, then $v+w=(a+d)i+(b+e)j+(c+f)k$ and that if $z$ is a constant, then $zv=(za)i+(zb)j+(zc)k$.
Also, the magnitude of a vector $v=ai+bj+ck$ is: $||v||=\sqrt{a^2+b^2+c^2}$.
Hence here: $||v||+||w||=||(3i-5j+2k)||+||(-2i+3j-2k)||=\sqrt{3^2+(-5)^2+2^2}+\sqrt{(-2)^2+3^2+(-2)^2}=\sqrt{9+25+4}+\sqrt{4+9+4}=\sqrt{38}+\sqrt{17}$.
