Answer
$-j$
Work Step by Step
We know that if $k=ai+bj$ and $l=ci+dj$, then $k+l=(a+c)i+(b+d)j$ and that if $z$ is a constant, then $zk=(za)i+(zb)j$.
Also, the magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$.
Hence here: $2v+3j=2(3i-5j)+3(-2i+3j)=6i-10j-6i+9j=-j$
