The Vector Equation of Lines | Multivariable Calculus

We've likely seen lines in 2D before, but how do we describe lines in 3 or more dimensions? In this video we will come up with a vector equation of lines that nicely generalizes what we've seen before in 2D. Effectively, to come up with an equation of a line you need two pieces of information, a point on the line and a direction vector along the line.
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[@n_2619]

5 minute-video from you yet a million times better than the one and a half hour lecture from my professor...thank you!

[@cheesywiz9443]

WOW.. this is exactly what I was looking for! Thank you so much for explaining what the equations actually mean. Instantly subscribed : )

[@rajhellskitchen3658]

Hey Dr Trefor, a wannabe physicist here. I just wanna say that your tutorials are AMAZING. Now any person with an internet connection, can access education at his/her finger tips. Thank you so much, you deserve much more subs...

[@beoptimistic5853]

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[@chaimaguechou3708]

Hello , how are going your studies , are you on the way ?

[@xiu8548]

1 video = few lectures + few handout materials from my professor. Thank you for your share!!!

[@beoptimistic5853]

ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐💐👍

[@alkankondo89]

Excellent and, again, UNIQUE approach for the equations of lines! I am really enjoying this series so far!!

[@adolfocarrillo248]

The format in your tutorials is nice. I´m axious to see that presentation explaining the combinatorial argument about the sum of N² natural numbers. Thanks for sharing

[@reganmian]

Stewart's Calculus has a nice amount of interesting practice problems , but feels like a calculus cook book. These videos are excellent in explaining the why

[@oitanny1213]

A big fat salute!!! Thanks a lot, that tv vector part was cherry on top of cake 💕

[@bingusiswatching6335]

I like the parallel to y=mx+b, the r0 is like a support for the whole thing like b is. And the v determines direction just like m

[@timotkeanu]

Thank you for the video. The illustrations were really helpful in understanding the concept

[@Phi1618033]

FYI, the 'g' in analogous is hard, as in gust, not just.

[@soorian6493]

In your accent

[@sladeberner6182]

​@@soorian6493 Yeah, and my accent is the correct and only important one. What's your point?

[@clarencechoy2382]

OMG I FINALLY GET IT!!!

[@DrTrefor]

love that feeling!

[@mukulbadhan5336]

this is exactly what i was looking for.. thanks

[@apou71]

thanks for helping me enrich my knowledge of vectors; A-levels will now be a breeze!

[@sduffxlr1549]

Thank you so much for explaining this so well!

[@DrTrefor]

Glad it was helpful!

[@moth36]

Thank you very much for your nice explanation

[@JonathanLang-nu2lx]

wow I understood this right away, thanks!

[@ashraf736]

WOW simply amazing.

[@aashsyed1277]

What is nice is that the parametric equation of the line extents to 2 dimensions

[@farhansadik5423]

So good man, you now havw yourself a devout follower 😂

[@Thebigbadskimachine]

I’m not gonna fail my midterm, thank you!!!!!

[@johnlee-dv3cd]

Do you have any recommended textbooks or problem sets? I am not in college but would like to practice and learn the courses. However, I found most online material out of date.

[@harshdarji1122]

I WANTED THIS VISUALISATION SO FREAKING BADD!!!! THANK YOU SO MUCH (Sorry for the caps right there...couldnt resist)

[@sinasoltan.m4859]

You are awesome .I am really waiting for your videos about vector calculus (line integrals, curl,...).LOVE FROM IRAN😚

[@beoptimistic5853]

ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐💐👍

[@malakasadalikhan109]

Po (point)--> starting from here (0>zero/origin) upto P (point) 3:50
vector from/btw Po and P is V or tV
Vectors r and ro are vectors from origin to the points P and Po resp.
4:45L

[@malefetsanekoalane4549]

Best.Thanks Herr Dr

[@matheusb.dambrowski4639]

Thanks for your videos!

[@DrTrefor]

My pleasure!

[@tanujpandey7702]

Thank you Dr. Trefor :)

[@bahaaedeenalghawel3041]

Thank you very much!
I hope you will make Arabic translation available in your wonderful and very useful videos.

[@camdenwyeth316]

Great video man, super super helpful :D

[@davida99]

AMAZING!!

[@ricki7389]

if I get the equation 2x_1+3x_2=0 how do I find the direction vector. im aware the normal would be (2 3) but what's the direction vector? I searched all over google but I couldn't find an answer.

[@NishchayG]

Thx for saving my life XD

[@lindaaa3299]

Thank you

[@beoptimistic5853]

ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐💐👍

[@Chelawu19]

👍 well done

[@steveying1305]

this is clear af

[@naveensingh5787]

sir can you explain why cartesian equation of a staright line have two equal symbols and have three terms

[@rockyjoe3817]

Keep up the great work

[@astha_yadav]

finallyyyy i get it thanks ಥ‿ಥ

[@tomdaliust531]

Sir, is it mean that the r node is the point where we start?

[@tomdaliust531]

to start on the line

[@continnum_radhe-radhe]

🔥🔥🔥

[@seemagangwar1313]

Wowwwwwwwww I got it

[@nicoaerts7257]

great tutorial, but please fix the echo

[@tomasbeltran04050]

Yayyyyyyyyy!!!

[@suhailawm]

tnx sr

[@beoptimistic5853]

ua-cam.com/video/XQIbn27dOjE/v-deo.html 💐💐👍👍

[@dhadbanjannarahari2071]

Why did we find r vector it only gives the position vector of point P .we need to find vector v since it is parallel to line ,equation of line and the vector v is same