Find a parametrization for the line segment joining the points.
-(0, 0, 0), (-2, -2, -4)
A) x = -2t - 2, y = -2t - 2, z = -4t - 4
B) x = -2t + 2, y = -2t + 2, z = -4t + 4
C) x = 2t, y = 2t, z = 4t
D) x = -2t, y = -2t, z = -4t

Question

Quizplus · Accepted Answer

A parametrization of a line segment between two points can be found by starting with the vector equation $\mathbf{r}(t) = \mathbf{r}_0 + t(\mathbf{r}_1 - \mathbf{r}_0)$, where $\mathbf{r}_0$ is the initial point, $\mathbf{r}_1$ is the terminal point, and $t$ varies between 0 and 1. For the points (0, 0, 0) and (-2, -2, -4), $\mathbf{r}_0 = (0, 0, 0)$ and $\mathbf{r}_1 - \mathbf{r}_0 = (-2, -2, -4)$, so the parametrization is $x = -2t$, $y = -2t$, $z = -4t$, which matches option D.

Find a Parametrization for the Line Segment Joining the Points