Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 667: 54

$⟨-\frac{4}{5},-\frac{8}{5}⟩$

Projection of $\textbf{u}$ along $\textbf{v}$ $=(\frac{\textbf{u}\cdot\textbf{v}}{||\textbf{v}||^{2}})\textbf{v}$ $\textbf{u}\cdot\textbf{v}=2\times1+(-3)\times2=-4$ $||\textbf{v}||^{2}=(\sqrt {1^{2}+2^{2}})^{2}=1^{2}+2^{2}=5$ Projection of $\textbf{u}$ along $\textbf{v}$ $=(-\frac{4}{5})\,⟨1,2⟩=⟨-\frac{4}{5},-\frac{8}{5}⟩$