Answer
$\sqrt {5}$
Work Step by Step
Let us consider two vectors $v=pi+qj$ and $w=xi+yj$; then we have: $v \pm w=(p \pm x)i+(q \pm y)j$
The magnitude of any vector (let us say $v$) can be determined using the formula
$||v||=\sqrt{p^2+q^2+r^2} $
Therefore, $||v +w||= ||(3i-5j) +(-2i+3j)|| \\
= ||i-2j || \\
= \sqrt {(1)^2+(-2)^2} \\ =\sqrt {5}$
