Consider two points located at \( \mathbf{r}_1 \) and \( \mathbf{r}_2 \), separated by a distance \( r = |\mathbf{r}_1 - \mathbf{r}_2| \). Find a time-dependent vector \( \mathbf{A}(t) \) originating from the origin, which is at \( \mathbf{r}_1 \) at time \( t_1 \) and at \( \mathbf{r}_2 \) at time \( t_2 = t_1 + T \). Assume that \( \mathbf{A}(t) \) moves uniformly along the straight line between the two points.
1
\( \mathbf{A}(t) = \left( 1 +\frac{t - t_1}{T} \right) \mathbf{r}_1 + \frac{t - t_1}{T} \mathbf{r}_2 \)
2
\( \mathbf{A}(t) = \left( 1 - \frac{t +t_1}{T} \right) \mathbf{r}_1 + \frac{t - t_1}{T} \mathbf{r}_2 \)
3
\( \mathbf{A}(t) = \left( 1 - \frac{t - t_1}{T} \right) \mathbf{r}_1 + \frac{t +t_1}{T} \mathbf{r}_2 \)
4
\( \mathbf{A}(t) = \left( 1 - \frac{t - t_1}{T} \right) \mathbf{r}_1 + \frac{t - t_1}{T} \mathbf{r}_2 \)