Answer
$\sqrt {117}$
Work Step by Step
To find $|2\textbf {V}-\textbf {W}|$, we first find $2\textbf {V}-\textbf {W}$ and then find the magnitude of this vector.
Finding $2\textbf {V}-\textbf {W}$:
Step 1: $2\textbf {V}-\textbf {W}$
Step 2: $2(-4\textbf {i}+\textbf {j})-(\textbf {i}-4\textbf {j})$
Step 3: $-8\textbf {i}+2\textbf {j}-\textbf {i}+4\textbf {j}$
Step 4: $-8\textbf {i}-\textbf {i}+2\textbf {j}+4\textbf {j}$
Step 5: $-9\textbf {i}+6\textbf {j}$
Now finding $|2\textbf {V}-\textbf {U}|$,
$|2\textbf {V}-\textbf {U}|=\sqrt {(-9)^{2}+6^{2}}=\sqrt {81+36}=\sqrt {117}$.
