Answer
$\sqrt{38}$
Work Step by Step
Perform the fubtraction first:
\begin{align*}
v-w&=(3i+j-2k)-(-3i+2j-k)\\
&=3i+j-2k+3i-2j+k\\
&=i(3+3)+j(1-2)+k(-2+1)\\
&=6i-j-k
\end{align*}
Recall that if $v=ai+bj+ck$, then the magnitude $||v||$ given by the formula:
$||v||=\sqrt{a^2+b^2+c^2}$
Hence,
\begin{align*}
||v-w||&=\sqrt{6^2+(-1)^2+(-1)^2}\\
&=\sqrt{36+1+1}\\
&=\sqrt{38}
\end{align*}
