Vectors: Vector Equation of a Line

Worked Solution:

The vector equation of this line is r = p + d where
p is the position vector of one point on the line and
d is a vector in the direction of the line,
As (a real number) varies, the position vector, r is a vector from the origin to every point on the line.
To find a point on the line 3 x = 8, y can be any value, say 0

the position vector of one point on the line is

( 0 )

To find a direction vector:
The line is parallel to the y-axis

( 0 1 )

is a vector in the direction of the line.

A vector equation of the line is r

=

( 0 )

+

( 0 1 )

This is not the only correct answer because we could have chosen
any other point on the line for p and
any other multiple of the direction vector, d, including negative multiples.