The vector equation r=r0+td\mathbf{r} = \mathbf{r}_0 + t\mathbf{d}r=r0+td describes:
A circle centered at r0\mathbf{r}_0r0
A line through r0\mathbf{r}_0r0 in direction d\mathbf{d}d
A plane with normal d\mathbf{d}d
A sphere centered at r0\mathbf{r}_0r0