# How do you write the vector equation that passes through point (-6,10) and parallel to <3,2>?

Aug 26, 2016

$r = < x , y > = < 3 t - 6 , 2 t + 10 >$

#### Explanation:

If a vector $V$ is parallel to the vector $U$, then $V = t U$, where t is

a scalar.l

Let $r = < x , y >$ be the position vector $O P$ to the point P(x, y) on

the line through A(-6, 10) in the direction of $< 3 , 2 >$. Then,

Vector $A P$

$= O P - O A$

$= < x + 6 , y - 10 >$

$= t < 3 , 2 >$, .

So, $r = < x , y > = < 3 t - 6 , 2 t + 10 >$