# How do you find the parametric equations of line that passes through the points (1, 3, 2) and ( -4, 3, 0)?

Oct 17, 2017

The equation is $\left(\begin{matrix}x \\ y \\ z\end{matrix}\right) = \left(\begin{matrix}1 \\ 3 \\ 2\end{matrix}\right) + t \left(\begin{matrix}- 5 \\ 0 \\ - 2\end{matrix}\right)$

#### Explanation:

Let the points be

$A = \left(1 , 3 , 2\right)$

$B = \left(- 4 , 3 , 0\right)$

The vector

$\vec{A B} = \left(\begin{matrix}- 4 \\ 3 \\ 0\end{matrix}\right) - \left(\begin{matrix}1 \\ 3 \\ 2\end{matrix}\right) = \left(\begin{matrix}- 5 \\ 0 \\ - 2\end{matrix}\right)$

The parametric equation of the line is

$\left(\begin{matrix}x \\ y \\ z\end{matrix}\right) = \left(\begin{matrix}1 \\ 3 \\ 2\end{matrix}\right) + t \left(\begin{matrix}- 5 \\ 0 \\ - 2\end{matrix}\right)$, $\forall t \in \mathbb{R}$