Vectors - Shortest Distance between Skew Lines : ExamSolutions Maths Revision
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- Опубліковано 6 сер 2015
- Tutorial on vectors and the shortest distance between skew lines
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This is the most brilliant explanation I have ever seen!! hats off!!
I've been searching since almost forever for a video that explains this concept intuitively and you're the only one who whom I found on UA-cam. I'm now a subscriber. keep it up :)
Had my results yesterday, and fortunately I got what I wanted and turned a U into a B and C, could not have done it without your website and tutorials. You're doing a great job and thought I'd come back and pay my gratitude. These videos actually help, fantastic job on them! Thank you very much.
Argh initially I was do damn confused as to how others derived this. But this explaination is just....simple and elegant.....That was amazing!
this is the best video on distance between skew lines that i have found. Thank you!
Had my results yesterday and fortunately was able to turn my U at AS, into a B at AS and C at A2 which were the results that have got me into a higher apprenticeship. I could not have achieved any of this if it hadn't been for your website and tutorials, thank you so much you are doing a fantastic job on them, please continue your work you are changing lives.
Thanks a lot for this wonderful explanation. Couldn't have done it better.
At 1:50 , it is not correct that purple Line is equal to yellow line because there exist only a single and unique shortest line of distance. So two are only possible if those two planes are parallel.
Thank you a lot for this video! Just one question ...what if the lines were not on parallel planes ? Would this method still be valid ?
+Wesam NasrEldin For any two non intersecting skew lines there will always be two planes that can be drawn through them that are parallel. Try taking two sheets of card and draw a line on each one. You will always be able to hold the pieces of paper apart so that the lines are skew and parallel.
absolutely love your videos
alright, this diagram made my day. you made the topic click for me! thanks a lot!
Thank you for the amazing visualisation👌
so trying to make sure i understood it correctly, if i were to make this in say unity, would it look something like this?
l1_start and l1_end are two points on line 1
l2_start and l2_end are two points on line 2
float distanceD = Vector3.Dot((l2_start - l1_start), Vector3.Cross(l1_end, l2_end) / Vector3.Cross(l1_end, l2_end).magnitude);
Very nicely and clearly explained.
clear explanation!
Wow 😲😲😲 a great explanation....loved from India 😍.... Highly thankful and better explanation than textbooks...
Thanks, now I got to know the derivation easily, which previously not able to imagine that.
amazing and very intuitive explanation
thank you sooooooo much!!! The video helps my IB math High level a lot!!!!!
Wonderful explanation ❤❤❤
Thank much sir
Really good.
Thank you so much, this was very helpful!
+Alexandra Tofful Thank you
brilliant explanation. which software you use for showing the planes and lines ?
good video i love it
After going through 20 videos or so on the other channels, I finally came across yours. I was finally able to clearly see how projection of vector (a2-a1) = d, Great graphics, nice work.
Cheers
Great explaination here. Thank you but what happens to cosine?
nice, keep it up mun
thank you thank you thank you!!!! beautiful solution, easy to follow!
Thank you for viewing.
Thank you - Pleased to hear that it helped
Thanks a lot
very helpful, thanks
THANK YOU
Very helpful! Thank you
That's good. Best wishes
Excellent teaching saved a lot of time
Hey, do you know what application you used for that diagram graphing calculator thingy
millions of thanks a lot sir. (from Srilanka)
This is so good. Thank you!!!!!!!!!!!!
Thank you and best wishes.
Best explanation
What about if the planes of lines aren't parallel? Projection of the known points isn't the same perpendicular shortest distance for all cases.
there is always a vector such that it is perpendicular to both direction vectors, essentially what it means is that a plane with that vector (n=d1×d2) as its normal can exist.
Thanks for this comment btw, it forced me to think as well. Also I will need to confirm this but for intersecting lines, a1•n=a2•n
thanks for vids, just one question , how did you derive (a1-a2) ?
Its position vector
thank you
sir is b1 and b2 in same plane? how can we do cross product b1xb2 if they are skew lines?
You know what ? I love you. Love from india.🙏🏻❤️...say JAI HIND JAI BHARAT.
when given an example with values how do I know what line to make l1 and l2?
the 3D model is so clear!!
+1 i was confused about the derivation but that made my concept crystal clear
Thank you
Thanks for this..I have been searching this topic since 3 days but none of them helped me...finally i got it. thanks again keep it up man...love from INDIA
Good job brother
Cheers
awesome
Hi sir, do you have any videos on growth and decay in C3?
Catherine Robinson Maybe this is what you are looking for www.examsolutions.net/maths-revision/core-maths/differentiation/exam-questions/Edexcel/C3/exp_ratesofchange.php
Isn't it the summer holidays? Go out and relax, you have the whole year to panic about exams!!!
Thank you, but i wanna ask u about the equal length of the blue and yellow line, it's equal if the shown planes are parallel, but if they are not parallel means they are not equal right? can u explain this please?
We can always draw 2 parallel planes passing through two different 'skew' lines .
thanks
Hello sir. Thank you for making this video because it helped me a lot to understand the concept. But I didn't get the part where we use unit vector to find the distance d.
1.Why do we have to use the unit vector?
2. After you've mentioned unit vector in the calculation, where did the cos theta go?
3. I understand that we need to find a vector that is perpendicular to both lines and planes, and hence the use of vector cross product. But if that's the case, why do we still need to multiply (a1-a2) with b1xb2/ |b1-b2| ? Don't we just need the vector cross product of the direction vectors alone?
1. We used a unit vector to bring in the cross product vector in the formula. Can you use another vector with some magnitude which doesn't change the initial terms?
2. After taking the magnitude of the unit vector, the term became the expansion of the dot product between a1-a2 and unit vector. You should learn dot product and see this video.
3. When we just take the cross product, we get a vector that is perpendicular to both planes but It may or may not coincide with the lines( like the blue vector d in the video) so we need to take the dot product of cross product and distance between the lines.
@@bhooveshwaran3590 hi, for 1) don’t you mean dot product*
thanks sir
You're welcome.
You are the best teacher of the world I have ever seen .I m also a mathematics teacher
Suddenly made a lot more sense thanks so much
That's what I like to hear.
your 3d illistration made it so eaasy.
❤❤❤❤❤
best。。。
Jus simple
Where is cos(theta) gone🤔
It replaced by dot product sign(.)
✨CrYstAl cLeaR✨
What if the planes aren't parallel?
Then the shortest distance wouldn't be the perpendicular distance between two planes, therefore you wouldn't be able to use right-angle trigonometry. Consider also that the distance will be zero if the planes eventually meet.
Though the planes would meet, the lines may not. If one of the lines were tilted slightly upwards , they still may not intersect but the planes will. How do i solve this?
I have the same question as Nathan. Does this question assume that two non intersecting lines are parallel or is this necessary for them to be non intersecting?
@@cianwalsh409 Nathan is correct that there are such cases where the planes aren't parallel, and the lines never intersect. However, there is an infinite number of planes that contain a fixed-line. So if you have two skew lines, then it is always possible to find two planes that are parallel to one another. This is the case that we consider in any example, and therefore you would use the same method in the video.
Saving ass
But a single line cannot describe a plane
Its just to show they're non planar
Had my results yesterday, and fortunately I got what I wanted and turned a U into a B and C, could not have done it without your website and tutorials. You're doing a great job and thought I'd come back and pay my gratitude. These videos actually help, fantastic job on them! Thank you very much.
Had my results yesterday and fortunately was able to turn my U at AS, into a B at AS and C at A2 which were the results that have got me into a higher apprenticeship. I could not have achieved any of this if it hadn't been for your website and tutorials, thank you so much you are doing a fantastic job on them, please continue your work you are changing lives.