Let $\mathbf{v}$ be a vector such that
\[\left\| \mathbf{v} + \begin{pmatrix} 3 \\ -1 \end{pmatrix} \right\| = 8.\]Find the smallest possible value of $\|\mathbf{v}\|.$
Question:
Let $\mathbf{v}$ be a vector such that
\[\left\| \mathbf{v} + \begin{pmatrix} 3 \\ -1 \end{pmatrix} \right\| = 8.\]Find the smallest possible value of $\|\mathbf{v}\|.$
Answer:
Let's think step by step.

user
8 - \sqrt{10}
Let $\mathbf{v}$ be a vector such that
\[\left\| \mathbf{v} + \begin{pmatrix} 3 \\ -1 \end{pmatrix} \right\| = 8.\]Find the smallest possible value of $\|\mathbf{v}\|.$
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