Unit vector of a line in straight line equation

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SUMMARY

The discussion centers on the concept of unit vectors in the context of straight line equations derived from two points, 'a' and 'b'. The expression b-a represents a vector along the line segment, while the equation b-a=d*t indicates that 'd' is a vector in the same direction as b-a. It is confirmed that 'd' can represent a unit vector if it is normalized, but it can also be any vector with the same direction. The magnitude of 't' is determined by the ratio of the magnitudes of b-a and d, leading to questions about the range of 't'.

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

 

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