Answer
$13i-21j+10k$
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:
$3v-2w\\
=3(3i-5j+2k)-2(-2i+3j-2k)\\
=9i-15j+6k+4i-6j+4k\\
=13i-21j+10k$
