The direction vector of a line given by a parametric equation $\vec{r}(t) = \vec{p} + t\vec{d}$ is $\vec{d}$. For the line $\vec{r}_{1}(t) = t \vec{i} + (-2t + 1) \vec{j}$, the direction vector $\vec{d}_1$ can be identified by looking at the coefficients of $t$ in
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