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.

****************************************************
YOUR TURN! Learning math requires more than just watching videos, so make sure you reflect, ask questions, and do lots of practice problems!
****************************************************

****************************************************
Other Course Playlists:

***************************************************

► Want to learn math effectively? Check out my "Learning Math" Series:

►Want some cool math? Check out my "Cool Math" Series:

*****************************************************

*****************************************************

*****************************************************

This video was created by Dr. Trefor Bazett

BECOME A MEMBER:

MATH BOOKS & MERCH I LOVE:

[n_]

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

[rajhellskitchen]

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...

[xiu]

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

[cheesywiz]

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

[alkankondo]

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

[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

[adolfocarrillo]

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

[oitanny]

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

[bingusiswatching]

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

[apou]

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

[sduffxlr]

Thank you so much for explaining this so well!

[mukulbadhan]

this is exactly what i was looking for.. thanks

[moth]

Thank you very much for your nice explanation

[JonathanLang-nulx]

wow I understood this right away, thanks!

[Phi]

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

[harshdarji]

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

[farhansadik]

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

[aashsyed]

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

[sinasoltan.m]

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