Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 667: 63

$\sqrt {17}$

Length of $\overline{OP}$= Component of $\textbf{u}$ along $\textbf{v}$= $\frac{\textbf{u}\cdot\textbf{v}}{||\textbf{v}||}$ $\textbf{u}\cdot\textbf{v}=⟨3,5⟩\cdot ⟨8,2⟩=3(8)+5(2)=34$ $||\textbf{v}||=\sqrt {8^{2}+2^{2}}=\sqrt {68}=2\sqrt {17}$ Therefore, Component of $\textbf{u}$ along $\textbf{v}$ $=\frac{34}{2\sqrt {17}}=\sqrt {17}$