Answer
$0$
Work Step by Step
Let us consider two vectors $v=pi+qj+rj$ and $w=xi+yj+zk$; 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, $||v||=\sqrt{(3)^2+(1)^2+(-2)^2} \\
= \sqrt {9+1+4} \\
= \sqrt {14}$
Also, $||w||=\sqrt{(-3)^2+(2)^2+(-1)^2} \\
= \sqrt {9+4+1} \\
= \sqrt {14}$
Now, $||v||-||w||=\sqrt {14}-\sqrt {14}=0$
