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 ;)
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.
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
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 😁
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.
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 :)
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 :)
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.
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.
+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.
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
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.
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!
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!
All i can say is that you the best teacher and you deserve flowers for that
You're a life saver. My calc 3 professor just isn't doing the job.
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!
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 ;)
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.
your 9 old video helped me understand much better and so faster than anyone else 😭thankyou!
this is by far the best explanation I could find to explain this.
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
I will cherish this treasure of a video forever… ❤
You don’t know how much I appreciate you lmao
You're subscribers should be 10m
you literally saved my life thankyou so much.mashallah
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 😁
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.
Thankyou so much for this! This was exactly what I needed to understand this abstract concept
thanks a lot for this video. following your graphical explanation, I was able to apply the same reasoning to a plane
You're a genius. Best explanation I got on this subject.
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 :)
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!
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
Glad I was able to see why the equation is what it is!
nicely explained, thank you for saving me
Thank you 👍 (very clear explanation as to why the vector equation works... was a bit confused coming from other youtube videos)
you saved me, thank you! so much better than my prof, please consider becoming a math teacher
You explained it way better than my Professor. Thanks man.
These subjects are so hard to understand with just my calculus book, so these videos are a real lifesaver!
BEST EXPLANATION!🙏🏾💙
Thank u sir,may u continue such humble duty
wow the picture example helped alot, thank you
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 :)
Thank you , this video helped a lot♥️♥️
Intuitive af. Will definitely subscribe
this video helped me so much!
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.
thanks, this stuff is very important while doing line integrals
The explanation helped me a lot.Thank you.
awesome video
Thank you for such a nice explanation.
really appreciate this video. you explain with simplicity!
You are absolutely goated
Thanks a lot bro thanks alot 😭😭🙏🙏
Thanks for this video! Really cleared up confusion!
Amazing video. Thankyou so much made it so much easier.
Better than Sal's explanation. Thanks!
so well explained! thanks a million!
VERY WELL EXPLAINED. THANKS.
this is very helpful!! thank you for making me understand better
This explanation so good
incredibly helpful, thanks g
I love u you are amazing a confusing start with a happy ending I have cleared my every confusion about this topic!
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.
Very good explanation.
Helped a lot sir thanks
Beast teacher u da real mvp
Very very helpful. Thank you!
Thank youuuu!!!so well explained
Very well explained thank you
Awesome video, thank you
It's even better than Sal's video im so impressed.
+KwanChun Lau Sal's video?
khan academy.
sal khan
Great explanation! Thank you!
Nicely done.
RUclips videos always better than Uni lmao
Thank you so much sir....
Thanks for visualization
Thnx a lot.. It was really helpful.
great explanation!
very helpful indeed, thank you.
thanks...awsome video
Ah yes, 13:37 saved my GPA. Thank u rootmath
Thank you so much.
Thank you! 👍
A super helpful video, short and precise!
How does one convert the vector or parametric equations to the Ax + By + Cz + D = 0 form?
Which software it is.?
I love u , total champion
Thanks!
so the vector equation is the equation of line L?
Does anybody know what tool @rootmath is using?
Hay, big fan of your videos, what software do you use to generate these videos? thanks
Man i fkn love you
Thank you!
great video
you the best
Thank you so much!
the position vector is count from the origin ?
show that the points (-2,3,5) and (1,2,3) (7,0,-1) are collinear by using slopes
Wonderful .
You the man!
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.
thank you for this
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.
Thanks a lot!!