application sphere of skewed line distance formula (curriculum mcv4u Ontario Canada, scripts for youtube video)

 slide 1

This video is to share some formula application of skew lines of Ontario Canada curriculum Calculus and Vectors coded as mcv4u. 

I also wrote a blog of this content at my blog site https://weifileandshare.blogspot.com/.

slide 2









slide 3

This slide is about the letter and symbol meaning of figure 1.


This video is to answer two questions about the application sphere of formula 1, and introduce how to use the formula to judge if two lines intersect or skew when they do not parallel or coincide.


The first question: may formula 1 be used for intersecting lines?

slide 4




slide 5

This slide is the reasoning process and distance d calculation expression of intersecting lines as I just now talked.

Since the calculation result is the same as the actual distance zero of intersecting lines, formula 1 can be used for intersecting lines.


The second question: may formula 1 be used for parallel or coincident lines?

slide 6






slide 7






slide 8

Now we use formula 1 to calculate the distance d between parallel or coincident lines. 




So formula 1 cannot be used for parallel or coincident lines.

slide 9

This slide is the reasoning process and distance d calculation expression of parallel or coincident lines as I just now talked.



Finally, may formula 1 be used to determine if two non-parallel or non-coincident lines skew or intersect?

It is easy to judge if two lines coincide or parallel. 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 zero, 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. The formula is also useful to judge if two lines intersect or skew when they do not coincide or parallel.


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