Answer
$-j-2k$
Work Step by Step
Let us consider two vectors $v=pi+qj+rz$ and $w=xi+yj+zk$. Then, we can write their sum as:
$v+w=(p+x)i+(q+y)j+(r+z)k$
The magnitude of any vector (let us say $v$) can be determined using the formula
$||v||=\sqrt{p^2+q^2+r^2} $
Therefore, $2v+3w=2 (3i-5j+2k)+3(-2i+3j-2k) \\
=6i-10j+4k-6i+9j-6k\\
=-j-2k$
