Unit vector of a line in straight line equation

[ahmed markhoos]

I know that for two points, the difference between them is a line segment

lets say these two points are 'a' and 'b' respectively, so b-a = "new vector represent the line"

In my textbook b-a=d*t -- where 'd' is a vector along the directon of 'b-a' and t is a parameter.

does 'd' actually represent the unit vector of the line? or it's just an arbitrary line with the same direction?

 

[Delta2]

Not necessarily the unit vector but any vector with the same direction. the absolute value of t is the magnitude of the vector b-a divided by the magnitude of the vector d.

 

[robphy]

Following up with https://www.physicsforums.com/members/delta.189563/'s comment, what is the range of t?