# How do you write the vector equation that passes through point (-1,4) and parallel to <6,-10>?

Jan 17, 2017

$\vec{r} = \left(\begin{matrix}- 1 \\ 4\end{matrix}\right) + l a m \mathrm{da} \left(\begin{matrix}6 \\ - 10\end{matrix}\right)$

#### Explanation:

The vector equation of a line in the direction of $\vec{D}$ passing through the point $\vec{A}$ is:

$\vec{r} = \vec{A} + l a m \mathrm{da} \vec{D}$

So the required equation in vector form is:

$\vec{r} = \left(\begin{matrix}- 1 \\ 4\end{matrix}\right) + l a m \mathrm{da} \left(\begin{matrix}6 \\ - 10\end{matrix}\right)$

Alternative notations are:

$\vec{r} = \left\langle- 1 , 4\right\rangle + l a m \mathrm{da} \left\langle6 , - 10\right\rangle$

Or,

$\vec{r} = \left(- 1 \hat{i} + 4 \hat{j}\right) + l a m \mathrm{da} \left(6 \hat{i} - 10 \hat{j}\right)$