Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 667: 61

$2\sqrt {2}$

Component of $\textbf{u}$ along $\textbf{v}$= $\frac{\textbf{u}\cdot\textbf{v}}{||\textbf{v}||}$ $\textbf{u}\cdot\textbf{v}=⟨3,2,1⟩\cdot ⟨1,0,1⟩=3(1)+2(0)+1(1)=4$ $||\textbf{v}||=\sqrt {1^{2}+0^{2}+1^{2}}=\sqrt 2$ Therefore, Component of $\textbf{u}$ along $\textbf{v}$ $=\frac{4}{\sqrt {2}}=2\sqrt {2}$