Answer
$\sqrt {38} $
Work Step by Step
Let us consider two vectors $v=pi+qj+rz$ and $w=xi+yj+zk$; then we have: $v+w=(p+x)i+(q+y)j+(r+z)k$
The magnitude of any vector (let us say $v$) can be determined using the formula
$||v||=\sqrt{p^2+q^2+r^2} $
Therefore, $v-w= (3i+j+2k)-(-3i+2j-k) \\
=3i+j+2k+3i-2j+k\\
=6 \ i-j-k$
Now, $||v-w||=\sqrt{(6)^2+(-1)^2+(-1)^2}\\=\sqrt {36+1+1}\\=\sqrt {38} $
