Application sphere of skew line distance formula (curriculum mcv4u Ontario Canada) and the formula use to decide if two lines intersect or skew

Application sphere of skew line distance formula (curriculum mcv4u Ontario Canada) and

the formula use to decide if two lines intersect or skew





  1. May formula 1 be used for intersecting lines?










The distance of intersecting lines is indeed 0. So, formula 1 can be used for intersecting lines.

  1. May formula 1 be used for parallel lines or coincident lines?









  1. May formula 1 be used to decide if two lines intersect or skew?

It is easy to judge if two lines coincide or parallel using their direction vectors. But how to judge

whether they intersect or skew if they do not coincide or parallel?

Usually we can use the equation system of the two lines. If there is a solution to the system, the lines

intersect. Otherwise, they skew.

With formula 1, we still have another method. If the distance is calculated 0, they intersect. Otherwise

they skew.


To sum up, formula 1 can be used for skew lines and also intersecting lines. But it cannot be used for

parallel or coincident lines. It is also useful for judging if two lines intersect or skew when we know

they do not coincide or parallel.




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