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The line $y = \frac{3x - 5}{4}$ is parameterized in the form $$\begin{pmatrix} x \\ y \end{pmatrix} = \mathbf{v} + t \mathbf{d},$$ so that for $x \ge 3,$ the distance between $\begin{pmatrix} x \\ y \end{pmatrix}$ and $\begin{pmatrix} 3 \\ 1 \end{pmatrix}$ is $t.$ Find $\mathbf{d}.$