# How do you write the vector equation that passes through point (1,5) and parallel to <-7,2>?

Jul 27, 2016

$< x . y > = < 1 , 5 > + k < - 7 , 2 >$, where k is arbitrary.

#### Explanation:

The parametric form of any vector parallel to $< - 7 , 2 >$ is $k \left(- 7 , 2\right) >$.

If #r = <x, y> is the position vector to the point R(x, y) on the line

through P(1, 5) that is parallel to $< - 7 , 2 >$, then the vector equation

of the line is

$< x . y > = < 1 , 5 > + k < - 7 , 2 >$, where k is arbitrary.

, using the addition law of vectors $O R = O P + P R$