$\mathsf{proj}_{\mathbf{a}}\,\mathbf{b}$
\begin{align*}
\mathsf{proj}_{\mathbf{a}}\,\mathbf{b} &= \left(\mathsf{comp}_{\mathbf{a}}\,\mathbf{b}\right)\dfrac{\mathbf{a}}{|\mathbf{a}|} \\
&= \left(\dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}|}\right)\dfrac{\mathbf{a}}{|\mathbf{a}|} \\
&= \left(\dfrac{11}{\sqrt{17}}\right)\dfrac{1}{\sqrt{17}}\langle 4,1 \rangle = \left\langle \frac{44}{17}, \frac{11}{17} \right\rangle
\end{align*}
\begin{align*}
\mathsf{comp}_{\mathbf{a}}\,\mathbf{b} &= \left|\mathsf{proj}_{\mathbf{a}}\,\mathbf{b}\right| \\
&= \left(\dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{a}|}\right) = \left(\dfrac{11}{\sqrt{17}}\right)
\end{align*}
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