Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 667: 59

$a\textbf{i}$

Projection of $\textbf{u}$ along $\textbf{v}=\textbf{u}_{||\textbf{v}}$$=(\frac{\textbf{u}\cdot\textbf{v}}{\textbf{v}\cdot\textbf{v}})\textbf{v}$ $\textbf{u}\cdot\textbf{v}=(a\textbf{i}+b\textbf{j}+c\textbf{k})\cdot \textbf{i}=a\times1+b\times0+c\times0=a$ $\textbf{v}\cdot\textbf{v}=1^{2}=1$ Then, $\textbf{u}_{||\textbf{v}}=(\frac{a}{1})\,\textbf{i}=a\textbf{i}$