<s>[INST] Vector magnitude subtraction Please help! This was in a textbook and I cannot seem to make sense of it. Would it not be 2?
The two vectors a and b are perpendicular. If a has magnitude 8 and b has magnitude 3, what is  |a−2b|??
I 
 [/INST] Since your vectors are perpendicular, they don't directly add and subtract like scalars would. 
Denoting them in R$^2$: 
$\textbf{a} - 2\textbf{b} = \begin{pmatrix}
8 \\
0
\end{pmatrix} - 
2 \begin{pmatrix}
0 \\
3
\end{pmatrix} = 
\begin{pmatrix}
8 \\
-6
\end{pmatrix}.$
Thus we need to consider what the value of $\begin{pmatrix}
8 \\
-6
\end{pmatrix}$.
Often, this is calculated with the Euclidean Distance, as $\left| \begin{pmatrix}
8 \\
-6
\end{pmatrix} \right| = \sqrt{8^2 + (-6)^2} = 10. $
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