Answer
$\sqrt {17}$
Work Step by Step
We have the vectors $v=<8,2>$ and $u=<3,5>$. Then:
$\textbf{u}_{\perp \textbf{v}}=\textbf{u}-\textbf{u}_{\parallel \textbf{v}}$
$\textbf{u}_{\parallel \textbf{v}}=(\frac{\textbf{u}\cdot\textbf{v}}{\textbf{v}\cdot\textbf{v}})\textbf{v}=(\frac{3\times8+5\times2}{8^{2}+2^{2}})⟨8,2⟩=⟨4,1⟩$
Then, $\textbf{u}_{\perp \textbf{v}}=⟨3,5⟩-⟨4,1⟩=⟨-1,4⟩$
$||\textbf{u}_{\perp \textbf{v}}||=\sqrt {(-1)^{2}+4^{2}}=\sqrt {17}$
