The projection of $\mathbf{a}$ onto $\mathbf{b}$ is given by
\[\frac{\mathbf{a} \cdot \mathbf{b}}{\mathbf{b} \cdot \mathbf{b}} \mathbf{b} = \frac{8}{2^2 + 6^2 + 3^2} \begin{pmatrix} 2 \\ 6 \\ 3 \end{pmatrix} = \boxed{\begin{pmatrix} 16/49 \\ 48/49 \\ 24/49 \end{pmatrix}}.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the projection of $\mathbf{a}$ onto $\mathbf{b} = \begin{pmatrix} 2 \\ 6 \\ 3 \end{pmatrix}$ if $\mathbf{a} \cdot \mathbf{b} = 8.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} 16/49 \\ 48/49 \\ 24/49 \end{pmatrix}
Find the projection of $\mathbf{a}$ onto $\mathbf{b} = \begin{pmatrix} 2 \\ 6 \\ 3 \end{pmatrix}$ if $\mathbf{a} \cdot \mathbf{b} = 8.$
test