Out of 3-4 videos I watched, this guy actually explained why we first must find a vector r to define the line l. Good job for actually teaching things well man, and thanks for the video.
This video was absolutely perfect. It was EXACTLY what I was looking to understand. My textbook (for vector calc) just gave us the definitions for the equation of a line in point direction form, threw in a graph, and expected us to be able to figure it out. Thank you, thank you. Your explanation was succinct and clear. I will probably end up watching many more rootmath videos after this one.
This is the best explanation of the vector form of a line I have seen so far. I have been trying to understand it for a long time. Some video I've watched was drawing parallels between vector form o a line and linear function which was quite confusing for me. Your teaching style facilitate learning by a big measure. Thank you!
I came here only becouse I know a youtuber that studies this topic at school in calculus. I just wanted to say that here in Italy (at least at the school I went in) we didn't discuss this topic, which is still a good one as a precourse for a uni physics course. We instead studied the equation of a line in a 2 dimension cartesian plane and other geometric figures again in 2d and that's it. We never discussed the 3d plane, but after seeing this video, I wish we did. Good luck with school from Italy ;)
Thank you! The textbook left me a definition and a mysterious formula x=td+p, which I can’t figure out what does it really mean after reading it many times. But 3 mins into this video, saved me maybe 5 hours of reading and thinking. Really ,Thank you! Subbed.
So easily explained man......I was getting frustated being unable to understand even after watching so many videos but your video cleared all the clouds of doubt. THAAAANKS A LOT 😁
Fun thing. I was watching Studypug before coming to this video. When I opened it, I got a Studypug advertisement saying that I could understand any math topic using Studypug :D I mean... there is a reason why I ended up watching this video. Well explained! Even if I just study math for fun, it's great no to go to bed before understanding such a cool topic :)
The best interpretation of line equation in vector form. The essential plays behind the equation is position vector that knowing the position vector is equivalent to knowing the coordinate of the line.
Thanks alot. cleared up alot questions for me. I really didn't understand why we were finding an arbitrary points position vector when we needed the equation of a line. but this cleared that up. thanks :)
I don't what to rewatch Khan's I just want something different. Atimes watching Khan's video need more concentration just like most people's video too. Kudos to Khan
+James Rockford Don't memorize, but understand. Once you understand, you can just think of the equation yourself. In my brain I only have to remember that a line requires a point and a vector, and that's all I need to create any linear equation.
Wonderful tutorial. Have a question: many other tutorials require 2 points to get the 3d equation of the line in vector and parametric form. Here instead you require a point and a direction vector. Can you expand on this all?
Two points will give you a direction vector since P1 - P2 = d is the direction between P1 and P2. Since you have 2 points you also, obviously, have 1 point. Thus 2 points is sufficient to find the equation of the line. Still though it is useful to think of a point and a direction as the minimal information you need.
Additional notes: The vector ''d'" need not be on the line.It is just any vector at any point in space to which the line "l" is parallel.You choose vector 'r' as any point on 'l' and make vector r - r(sub0) = t.d [ 't' times vector 'd' ]where t is a variable rational number.This provide the vector equation.
t is just a variable representing a number, you can pick any letter you want. You do need *something* where t is to represent how far along the direction vector you want to move (how much you want to scale the direction vector)
Out of 3-4 videos I watched, this guy actually explained why we first must find a vector r to define the line l. Good job for actually teaching things well man, and thanks for the video.
Sometimes, a small example with a picture is better than dozens of pages of proofs and theorems.
What dozens if proofs and theorems?
seriously bless these youtube tutorial people, y'all have rescued my degree (and my career) more times than I can remember
This video was absolutely perfect. It was EXACTLY what I was looking to understand. My textbook (for vector calc) just gave us the definitions for the equation of a line in point direction form, threw in a graph, and expected us to be able to figure it out. Thank you, thank you. Your explanation was succinct and clear. I will probably end up watching many more rootmath videos after this one.
Elanna Crook Same, textbook made me completely stuck with the definition w/o any explanation. Great video, very helpful.
oh my gosh. i'm totally with you as well. this video help me understand what's really happening conceptually and at a DECENT pace! THANK YOU SO MUCH!
Lana P Same.
2mins into your video, I subscribed b/c everything you explained in the first 2mins made more sense than a whole hour with my calculus III professor!
Thanks for the sub!
i was about to break down right before i found this video - THANK YOU SO MUCH!
All i can say is that you the best teacher and you deserve flowers for that
This is the best explanation of the vector form of a line I have seen so far. I have been trying to understand it for a long time. Some video I've watched was drawing parallels between vector form o a line and linear function which was quite confusing for me. Your teaching style facilitate learning by a big measure. Thank you!
your 9 old video helped me understand much better and so faster than anyone else 😭thankyou!
Thanks man! I love that you explained clearly in the beginning why it's calculated like that not just how it's calculated. It made much more sense!
You're a life saver. My calc 3 professor just isn't doing the job.
I came here only becouse I know a youtuber that studies this topic at school in calculus. I just wanted to say that here in Italy (at least at the school I went in) we didn't discuss this topic, which is still a good one as a precourse for a uni physics course. We instead studied the equation of a line in a 2 dimension cartesian plane and other geometric figures again in 2d and that's it. We never discussed the 3d plane, but after seeing this video, I wish we did.
Good luck with school from Italy ;)
this is by far the best explanation I could find to explain this.
Thank you! The textbook left me a definition and a mysterious formula x=td+p, which I can’t figure out what does it really mean after reading it many times. But 3 mins into this video, saved me maybe 5 hours of reading and thinking. Really ,Thank you! Subbed.
And my professor didn’t explain many essential things during zoom lectures. Sad.
You're subscribers should be 10m
Thank you! This was very useful for my IB HL Maths Revision :)
Victor Rodionov shared suffering
ohhhhh how I hate the IB
For real dude, finals in less than a month..
@Main Engie math HL paper 1 was easy, paper 2 was alright, and paper 3 was good, all in all I think I'm getting a 6, but possibly even a 5
So easily explained man......I was getting frustated being unable to understand even after watching so many videos but your video cleared all the clouds of doubt. THAAAANKS A LOT 😁
Fun thing. I was watching Studypug before coming to this video. When I opened it, I got a Studypug advertisement saying that I could understand any math topic using Studypug :D I mean... there is a reason why I ended up watching this video. Well explained! Even if I just study math for fun, it's great no to go to bed before understanding such a cool topic :)
Thankyou so much for this! This was exactly what I needed to understand this abstract concept
You explained it way better than my Professor. Thanks man.
You're a genius. Best explanation I got on this subject.
These subjects are so hard to understand with just my calculus book, so these videos are a real lifesaver!
I will cherish this treasure of a video forever… ❤
Perfect, excellent explanation
Didn't understand the purpose or intention of the direction vector from my textbook. This video cleared that up a lot for me!
The best interpretation of line equation in vector form. The essential plays behind the equation is position vector that knowing the position vector is equivalent to knowing the coordinate of the line.
you literally saved my life thankyou so much.mashallah
You don’t know how much I appreciate you lmao
thanks a lot for this video. following your graphical explanation, I was able to apply the same reasoning to a plane
nicely explained, thank you for saving me
Thanks alot. cleared up alot questions for me. I really didn't understand why we were finding an arbitrary points position vector when we needed the equation of a line. but this cleared that up. thanks :)
you saved me, thank you! so much better than my prof, please consider becoming a math teacher
Glad I was able to see why the equation is what it is!
Thank u sir,may u continue such humble duty
who came here after struggling with khan's explanation?
me
Me
Me too, I just came. Khan is great, very great but no one knows all. Khan tried.
I don't what to rewatch Khan's I just want something different. Atimes watching Khan's video need more concentration just like most people's video too. Kudos to Khan
hahahaha its me as well
Intuitive af. Will definitely subscribe
Thank you 👍 (very clear explanation as to why the vector equation works... was a bit confused coming from other youtube videos)
BEST EXPLANATION!🙏🏾💙
this is great in simple explanation of three dimensional line presentation
thank you very much....I spent too much time looking for a good explaining.
The explanation helped me a lot.Thank you.
awesome video
this video helped me so much!
thanks, this stuff is very important while doing line integrals
Thank you for such a nice explanation.
Thank you , this video helped a lot♥️♥️
really appreciate this video. you explain with simplicity!
VERY WELL EXPLAINED. THANKS.
This explanation so good
Amazing video. Thankyou so much made it so much easier.
so well explained! thanks a million!
I love u you are amazing a confusing start with a happy ending I have cleared my every confusion about this topic!
Very good explanation.
Helped a lot sir thanks
Better than Sal's explanation. Thanks!
Nicely done.
Hay, big fan of your videos, what software do you use to generate these videos? thanks
It's even better than Sal's video im so impressed.
+KwanChun Lau Sal's video?
khan academy.
sal khan
this is very helpful!! thank you for making me understand better
Thanks for this video! Really cleared up confusion!
You are absolutely goated
Thanks a lot bro thanks alot 😭😭🙏🙏
good tutorial... Curious... is that formula at 8:10 a standard equation I should memorize? and it works for all similar problems?
thanks
+James Rockford Don't memorize, but understand. Once you understand, you can just think of the equation yourself. In my brain I only have to remember that a line requires a point and a vector, and that's all I need to create any linear equation.
incredibly helpful, thanks g
Very very helpful. Thank you!
Very well explained thank you
How does one convert the vector or parametric equations to the Ax + By + Cz + D = 0 form?
Awesome video, thank you
Great explanation! Thank you!
Wonderful tutorial. Have a question: many other tutorials require 2 points to get the 3d equation of the line in vector and parametric form. Here instead you require a point and a direction vector. Can you expand on this all?
Two points will give you a direction vector since P1 - P2 = d is the direction between P1 and P2. Since you have 2 points you also, obviously, have 1 point. Thus 2 points is sufficient to find the equation of the line. Still though it is useful to think of a point and a direction as the minimal information you need.
so the vector equation is the equation of line L?
Thnx a lot.. It was really helpful.
Beast teacher u da real mvp
Thank youuuu!!!so well explained
Thank you so much sir....
great explanation!
thanks...awsome video
Thanks for visualization
"in direction of" 9:15 is synonymous with parallel in 3d space right
Yes, that's correct!
Which software it is.?
Ah yes, 13:37 saved my GPA. Thank u rootmath
the position vector is count from the origin ?
great video
very helpful indeed, thank you.
Additional notes: The vector ''d'" need not be on the line.It is just any vector at any point in space to which the line "l" is parallel.You choose vector 'r' as any point on 'l' and make vector r - r(sub0) = t.d [ 't' times vector 'd' ]where t is a variable rational number.This provide the vector equation.
what is t exactly and why you should use it here ?
t is just a variable representing a number, you can pick any letter you want. You do need *something* where t is to represent how far along the direction vector you want to move (how much you want to scale the direction vector)
If I am given two points, which one should I start with. When I try both, different answer comes out
In 3 dimensions a line does not have a unique representation so both answers are right (assuming you did all the steps in between correctly)
Thank you very much!
Thank you so much.
Thank you! 👍
you the best
What app is that please?
The drawing program is Gimp, it's free and open source
UA-cam videos always better than Uni lmao
A super helpful video, short and precise!
I love u , total champion
Does anybody know what tool @rootmath is using?
Man i fkn love you
Hey there!!!
how to make this type of video?
Thank you!
Thanks!
Wonderful .
Honesty going from sequences and series and fancy integration techniques this is not that bad
Honestly*
Good luck to everyone in calc 3 this semester!