Vector and Parametric Equations of a Line (Line in 3 dimensions)

In this video we derive the vector and parametic equations for a line in 3 dimensions. We then do an easy example of finding the equations of a line.

[BangMaster]

Sometimes, a small example with a picture is better than dozens of pages of proofs and theorems.

[lukedierks]

seriously bless these youtube tutorial people, y'all have rescued my degree (and my career) more times than I can remember

[kevinhenry]

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!

[elannacrook]

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.

[pcr]

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.

[Emmelifall]

i was about to break down right before i found this video - THANK YOU SO MUCH!

[peanutkix]

You're a life saver. My calc 3 professor just isn't doing the job.

[nicholasachuz]

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!

[lman]

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 ;)

[BoZhaoengineering]

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.

[sak.]

your 9 old video helped me understand much better and so faster than anyone else 😭thankyou!

[LezendFacts]

nicely explained, thank you for saving me

[timiakogun]

who came here after struggling with khan's explanation?

[firomsamohammed]

you literally saved my life thankyou so much.mashallah

[mohammedamayri]

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!

[jackthehack]

thanks a lot for this video. following your graphical explanation, I was able to apply the same reasoning to a plane

[jordanjenkins]

Didn't understand the purpose or intention of the direction vector from my textbook. This video cleared that up a lot for me!

[prathvisingh]

So easily explained 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 😁

[jamesrobertson]

this is by far the best explanation I could find to explain this.