Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D
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- Опубликовано: 12 сен 2024
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Deciding if Lines Coincide, Are Skew, Are Parallel or Intersect in 3D. Here I describe two lines in 3space using parametric equations. We have to decide if they coincide, are parallel, are skew or if they intersect in exactly one point.
It's not just intersection. Sometimes, I feel like there's no point of anything.
that escalated quickly
Those were dark, depressing times. I'm glad I'm done with all my calculus courses, and that wouldn't have been possible without the amazing PatrickJMT. I kind of miss calculus now, to be honest...
Hahahahahaha for real
this is calculus? lol i never knew that
This is calculus? Wtf
When two lines are skew, it means that the two lines DO NOT intersect nor are they parallel. Hence, prove that they are not parallel and that they do not intersect and you've proved that they are skew! I hope this helps! :D
patrick, thank you for all your videos! you've saved me through calc 1, 2 and now 3!
I learn more watching Patrick and Khan than i do in class.
Same here xd
+aten747 what class......
my prof suck
Your suppose to self learn, that's how my highschool works and uni will too.
excuse me, what if there is a solution for this set of two equation then what are we gonna do, are you gonna evaluate the two site of the third equation using the values of t and s from the first two? Can you have another example where there is a solution then what's next? Thanks a ton
One more thing.. I have been watching videos on youtube for a long time when I need help with stuff that I don't understand. Your videos are by far THE BEST that I have seen on RUclips. Your explanations are simple but at the same time you outline the crucial things that correlate to that chapter/subject. I just wish you taught other classes as well!!
Hey Patrick, Could you go through examples proving the lines skew, intersect, or coincide?
Salvatore Angrisani Basically, it goes like this:
Parallel + Intersect = Coincide
Parallel + Not Intersect = Parallel
Not Parallel + Intersect = Intersect
Not Parallel + Not Intersect = Skew
+Salvatore Angrisani not intersect + not parallel (their vectors are't multiples of each other)=skew
Thanks, dude!
@@cameodamaneo How could they be parallel and intersect? if they're parallel they should not intersect
@@lerevenger000 They coincide, as I said.
Hi Patrick,
I would just like you to know that I watched all your videos for Calculus II while I was taking it in the summer and it helped me immensely. You really helped me understand the material more efficiently and I was able to work out problems and get them right when I did them your way. For one of my problems in my multivariable book, I got t=s after I worked it out. The answer is that the L1 and L2 are skew but I don't understand why. Hopefully I can understand better if you explain.
thank you! Will you please show an example of when you get a true statement after plugging into the second equation?
I have to submit my assignment after few hours, you saved my life. thank you
spread the word :)
Really thnx to Patrick for making all these fabulous videoes...You have saved me so many time on my Calculus Hw..
Yes you are correct, because by definition the cross product is defined by the angle separating the two vectors. || a x b || = ||a|| ||b|| sin(x) Hence if your direction vectors for your two lines are parallel, the angle will be 0. Sin(0)=0, hence || a x b || =0.
To decide if the lines coincided, would it be simpler to do the following?
Let t = 0, then the point (1,3,1) is on L1
Is (1,3,1) on L2? To get the x coordinate of L2 to equal 1 we set s = 2
But s = 2 doesn't give a L2 y coordinate of 3, so the lines do not coincide.
if there is no point of intersection, the lines can be or not be parallel. If they were planes they must be parallel.. Am I wrong?
+EeDymonNij you are right, it might be parallel or can be skew, you need to compare the direction vector in both L1 and L2 in this example Patrick using for L1 and for L2, here is the trick, if direction for L1 and L2 are scalar multiple of each other, then they are paralllel, in this case it is , if you multiple -1 to L1 you will get L2, thus those 2 lines are parallel instead of skew HOPE IT HELPS XD and excuse my bad English
+EeDymonNij He used only 2 equations so essentially making it a 2D plane.
what about skew line?
They are skew lines if they are neither parallel nor intersecting
James Stewart Calculus book has less detail than Patrick. This is great. Thank you
I just realized... is that a sex doll in the left corner of your profile pic? LOL you're still the best!
You save my life every time with these videos
my internet is really slow right now, it takes 10 mins to load this video lol but i sit through the 10 mins to watch it with pauses because your explanation is the best! :) thank you so much!
what happened since last 9 years
is there a way to search through just your vids for a specific topic?
Thank you again patrick!!
Hi Patrick , how did you get { t =-2-s } ? I think you made a mistake I am getting { 2t = 2s }.
Is there a part 2 for this video?
notice how he does it in Sharpie. Because this guy is such a boss he doesn't make mistakes..
He uses whiteboard sometimes though ^^ Quite useful when you simplify a lot to spare board space ;)
If there isnt a solution couldnt that also mean that the lines are skew but not parallel?
I believe the answer to this is because they are scalar multiples of each other. However, if in doubt on an exam, you could take the cross products of the two direction vectors. If you get zero, you would confirm that they are parallel.
Very well explained thankyou
This is great man!!
What if there's no coefficient value, that makes it 1, right?
Many thanks .. Are the papers that explain the existence of the form of PDF😊
I'm only in High School, but I think I'm going to pass my Calculus class thanks to you !
Another great video!
They don't intersect so they are parallel??? What about skew lines: They don't intersect and they are not parallel
Can sb explain me why he made that affirmation?
You are fantastic thanks for saving my life
your a life saver sir
Wow this has saved me after I day dreamed in class during the explanation aha cheers
goat math channel
how to determine the equation is skew??
so is both the lines in the video coincide?
Patrick, how can I determine that lines are skew?
If they are not parallel and they don't intersect, then they are skew
Got it thanks!
0:50 how he move the words?????
was just watching arrested development and holy shit you sound like Tobias :P
thank you for saving me from IB HL math AA
He most likely does them BEFORE making a video so he is much more prepared.
go on there innit
gonna go around to ppl's houses preaching about our lord and saviour, patrick, now
Thank you!
nope. if the dot product of the vectors = zero then they're perpendicular, Quinn was right.
If the lines were coincident though, there wouldn't be just one point of intersection, all the points would intersect, which means that there are an infinite number of solutions to the method described in the video if the lines were coincident.
YOU MAKE LIFE BETTER
thankyou!
MAN THAT"S VERY GREAT
at the end he should have said "if there is no point of intersection the lines are either parallel or skew"
interesting...thanks to you
Ty
AFTER 11 YEARS
ありがとうございます!
If they are scalar multiples they will always be parallel
He's writing on paper, it wrinkles as he writes.
this title is misleading what about telling if they were skew or if they do intersect
Wrong! :-)
In 3D space, "no point of intersection" does not mean "lines are parallel".
it means skew thank you
Last example lines are skew not parallel
You are poor in maths Improve speed of your calculations
i will work on harder on me maffs