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\mathbf{a} \cdot \mathbf{a} = 1^2 + 1^2 + 1^2 = 3
Thus, the projection is:
\text{proj}_{\mathbf{a}} \mathbf{r} = \frac{11}{3} \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} = \begin{bmatrix} \frac{11}{3} \\ \frac{11}{3} \\ \frac{11}{3} \end{bmatrix}

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