Chapter 13 - Vector Geometry - 13.3 Dot Product and the Angle Between Two Vectors - Exercises - Page 667: 53

$⟨\frac{7}{2},\frac{7}{2}⟩$

Projection of $\textbf{u}$ along $\textbf{v}$ $=(\frac{\textbf{u}\cdot\textbf{v}}{||\textbf{v}||^{2}})\textbf{v}$ $\textbf{u}\cdot\textbf{v}=2\times1+5\times1=7$ $||\textbf{v}||^{2}=(\sqrt {1^{2}+1^{2}})^{2}=1^{2}+1^{2}=2$ Projection of $\textbf{u}$ along $\textbf{v}$ $=(\frac{7}{2})\,⟨1,1⟩=⟨\frac{7}{2},\frac{7}{2}⟩$