# How do you write the vector equation that passes through point (3,-5) and parallel to <-2,5>?

Nov 3, 2016

$\vec{r} = \left(3 - 2 \lambda\right) \vec{i} + 5 \left(\lambda - 1\right) \vec{j}$

#### Explanation:

the vector equation of a line is given by;

$\vec{r} = \vec{a} + \lambda \vec{d}$

where:

$\vec{a}$ is a known point on the line
$\vec{d}$ is the direction of the line.

in this case:

$\vec{a} = < 3 , - 5 >$

$\vec{d} = < - 2 , 5 >$

so we have $\vec{r} = \left(3 \vec{i} - 5 \vec{j}\right) + \lambda \left(- 2 \vec{i} + 5 \vec{j}\right)$

$\vec{r} = \left(3 - 2 \lambda\right) \vec{i} + 5 \left(\lambda - 1\right) \vec{j}$