Unit vector of a line in straight line equation

In summary, the difference between two points, 'a' and 'b', is a line segment represented by the vector b-a. This vector can be written as d*t, where 'd' is a vector along the direction of b-a and t is a parameter. The value of 'd' does not necessarily have to be a unit vector, but it must have the same direction as b-a. The magnitude of t, or |t|, represents the magnitude of b-a divided by the magnitude of d. The range of t is not specified and can vary depending on the specific problem.
  • #1
ahmed markhoos
49
2
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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  • #2
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.
 
  • #3
Following up with https://www.physicsforums.com/members/delta.189563/'s comment, what is the range of t?

 

Related to Unit vector of a line in straight line equation

What is a unit vector?

A unit vector is a vector with a magnitude of 1. It represents the direction of a given vector without taking into account its length.

How do you find the unit vector of a line in a straight line equation?

To find the unit vector of a line in a straight line equation, you first need to determine the direction of the line by calculating the slope. Then, divide the coefficients of the variables by the calculated slope to get the components of the unit vector.

Why is the unit vector important in a straight line equation?

The unit vector is important in a straight line equation because it helps to represent the direction of the line without being affected by the length of the vector. This allows for easier calculations and comparisons between different lines.

Can a unit vector have a negative magnitude?

No, a unit vector must have a magnitude of 1, so it cannot have a negative magnitude. However, it can have negative components depending on the direction of the line.

Is the unit vector unique for a given line?

Yes, the unit vector is unique for a given line. While there can be multiple lines with the same slope, the unit vector will have different components for each line, making it unique.

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