Introduction to Vectors and Their Operations

At this point we've pretty much mastered numbers, but there is another mathematical construct that will important to learn about, and that's vectors! What is a vector? What is a scalar? How do they differ? What can we use vectors for? Find the answers to all these questions right here!
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[@San-kq1ss]

your method of teaching proves why textbooks do not need hundreds of pages

[@equinoxboy]

too good to be true
lol

[@Moltenlava]

i disagree though, textbooks more than often provide more explanation to the topic's discussed, granted they are hard to read if you're just trying to revise or prepare for an exam

[@leonardchung3825]

@@Moltenlava I fall asleep on textbooks. You only need textbooks for the practice questions, there are more than enough videos on YT to explain them.

[@ahahaohoho83]

I raise my hat to you good sir

[@ryacoli]

Apart from the exercises.

[@aidat7657]

I couldnt understand all these things by myself while reading textbooks,and now after whatching your video I got it. I am so relieved and thankful to you that I even wanna cry. Thank you, Professor!!!

[@alexTillery]

I struggle so much with vectors, and I don't know why. These videos really help me understand a lot though, and I appreciate them a lot.

[@omerkaya545]

The vector knows where it is, at all times.
It knows this because it knows where it isn't.
Subtracting where it is from where it isn't, or where it isn't from where it is...

[@asshivam8117]

You are life savers for folks like me who are preparing for IIT entrance exams without any coaching. Keep going Professor.👍👍

[@codegenesis80085]

Wow I am too :)

[@a.pal_yt2018]

Man, I'm too. Pls some motivation.

[@tennesseeonruang9600]

Stunning! It's been a year, how did it go?

[@adityasamani4299]

lmao me too just started this month

[@lewisoutten1610]

@@a.pal_yt2018 U don't

[@overlordprincekhan]

The fact I love about this channel is that this guy teaches stuffs straightcut and precisely to the point

[@maloryknoxx666]

Great content as usual. Some of these professors aren't good at explanations. Your 10 minute video just saved me from 5 power point slides with no actual examples, just letters and graphs. Thank you.

[@milespq5561]

When my teacher explained this, I had no clue what he was taking abt. Then I watch this video, and I realize it’s mad easy😂

[@sergionaranjogomez6740]

I liked how you explain.
Well done, professor.

[@grishikesh102]

Ur videos are very helpful for me I just watch them a day before my tests!!!! 😅😅

[@friscianviales7519]

Good stuff professor; thanks for sharing!

[@himanshupandey1480]

Waiting for this for so long 😍

[@davysong9488]

So simple, concise, yet providing so much information and reinforcing many basic, misleading concepts! 10-minute video=2 hours-worth textbook reading!!!!

[@osamashawky622]

I never seen such a fantastic way of explaining things

[@quahntasy]

Very helpful video!

[@Retrograde.Amnesiac]

Thank you for this video, professor! :)

[@equinoxboy]

Reject Zoom Classes
Return to Professor Dave Explains...

[@yomnaislam948]

I have a physics exam tomorrow and this just made everything easier, thank you

[@savanrathod6021]

Thanks professor, it helped a lot.

[@anysianas5099]

You’re the best professor Dav thank you 🙏🏾 so much

[@mithila1321]

Thanks… It helped me a lot… My book took 20 pages or maybe more than that to describe this simple thing ( As from your video , I found it simple so far ) , which you did just in 10 minutes❤️

[@c.thayammalgeetha6734]

Thanks for the teaching sir

[@therunkumar]

More and more people like you should fill my recommendation feed.

[@63pity99]

Why it's so easy to understand but the book tells otherwise lol. Thanks for this. This saves me up from my lab simulation today

[@alewarten]

Subscribed. Thank you!

[@AwakouMadul]

Thanks you so much teacher
You have explained it in good way❤❤

[@ngangaedith8169]

IT'S HELPFUL

[@mousetrapstudios]

Thank you! Thank you! Thank you!

[@pierrekanti]

Thank you so much ❤️

[@sriram-mh4qb]

even i am feeling lucky bcoz tommorow is my test on vectors

[@sparkxite]

THANK YOU CHEMISTRY JESUS YOURE A LIFE SAVER

[@farhanfouadacca]

Nice review

[@easy-peasy9906]

What is the detailed difference between geometric and algebraic vectors?

[@doncheedleismydad4540]

If the textbooks just kept it simple, life would be so much easier. Thank you, Professor Dave.

[@Lamplovr]

My fav channel

[@vaibhavsharma226]

Increase the Volume

[@roylagat890]

Absolutely goated 👌🙌

[@prem_ningombam]

thank you

[@axis1198]

Most of you here learn better listening to someone enthusiastically explain, than reading textbooks.

[@drunkieowl2207]

Is this gonna be a start for a Multivariable Calculus series?

[@ProfessorDaveExplains]

calculus is over! i did a couple multivariable with the finding volumes of solids of revolution and what not.

[@acethemain7776]

professor dave's the ultra instinct form of education

[@equinoxboy]

smh

[@shegawsendekhailie2223]

You are so genius

[@jagruti_rs]

Awh our.. saviour!! 🙏 Owe ya'
Keep spreading genius.. and so the smiles🌈

[@uzomajoe8354]

@professor dave, the 3 dimensional coordinate system in 7.24, the x,y,z axis should be swapped. i.e x should be where y currently is, y should be where x currently is, and z should be where x currently is..at least, that's how i have seen it depicted in other books...except this does not matter

[@carultch]

As long as you pick a right-handed coordinate system, you are free to assign whichever variable you want to the three axes of space. Both the coordinate system you describe, and the coordinate system Dave is using, are right-handed coordinate systems. One where i cross j = k. One where you can place your right pointer finger on +x, right middle finger on +y, and right thumb on +k. That is, unless you are given a coordinate system in a problem, in which case you should solve within that coordinate system to be on the same page with the problem author.
While in concept, you can use left-handed coordinate systems, this is generally not recommended. It is convention to use right-handed coordinate systems, and operations like the cross product only work the way we are taught, if you use a right-handed system. If you try a left-handed system, not only will you confuse yourself, but also the person reading your work.

[@Topclassic168]

Good Idea.

[@jojololo752]

The fuck you mean to tell me that I've been sitting here all day panicking and crying over basic algebra because my brain didn't process that it was basic algebra until he told me it was
thank you professor dave god bless

[@aadithyahrudhay2269]

Thanks for the video, but what is the proof for all these laws? They make sense and are simple in concept, but what is the garuantee/proof that putting the vectors in a triangle/parallelogram give us the resultant?
Thanks.

[@fatimalearns9618]

Maybe, these are just the methods scientists could develop for getting accurate answers since they cannot perform normal mathematical rules upon themthat are used for scalars. Idon't really know, just a student here.

[@aadithyahrudhay2269]

@@fatimalearns9618 hey, forgot I posted this comment, but I think I got an answer. Seems kinda foofy, but here's my reason:
So all these manipulations make perfect sense for displacement, cuz it is after all length, and the geometry works for lengths.
So, if it makes sense for displacement, won't it work for say displacement in a period of time? Hence it's justifiable for velocity, and similarly acceleration.
So I thought what if all vectors have displacement (and the basic involvement of length)? And I searched and searched and found that all vectors have length in some way or the other.
Tldr: it works for displacement/distance (cuz geometry) and since all the vectors I know have length involved with some other scalars like mass, charge, etc. that proportionality still holds good.
Hope that makes sense! (I recognize my arguments crumble if you find a vector which doesn't have length/, distance in it, so lemme know if you find any).

[@fatimalearns9618]

Thankyou so much for a good explanation. I did not know you would reply back.🥺
The vectors I know about, do have length as you said, in a way that they involves displacement and distance covered. ✨

[@aadithyahrudhay2269]

@@fatimalearns9618 glad to help!

[@fatimalearns9618]

@@aadithyahrudhay2269 what are you studying 📚 now btw?

[@gokulkrishnan2179]

Tq so much

[@camellemons3737]

how many of that shirt do you have? or has one lasted all this time. thanks for everything. i owe my grades to you.

[@ProfessorDaveExplains]

that's the math shirt! once i start a new playlist i stick with a shirt until the bitter end

[@habibaelhadad1000]

Luv u Dave
N I luv your videos

[@gyanadityaranveergautam4313]

miracle sir

[@chinzhishengmoe]

Hi professor Dave, I need to know what name of font do you use in your video. Please reply me.

[@ProfessorDaveExplains]

gotham bold

[@Garomsa-sp2cb]

Hi brother thank you Country ethiopian

[@hubertshellington8198]

yo nice vid

[@jabadabaduu.]

Love you

[@yevseldev]

Legend

[@kuuly3334]

0:25 OH YEAHHH

[@swedishpsychopath8795]

I'm normally a genius but I'm stuck here. I'm trying to calculate this mentally (in my head) WITHOUT using any tools incl. pen + paper. If you connect i, j, k with lines to form a plane this plane becomes the bottom of a pyramid: What is the VOLUME of the pyramide if the top of the pyramide is in Origo? (since i,j,k are unit vectors, each with length 1 obviously the volume will be less than 1, and definitely less than a half) I'm hoping the volume will be a nice fraction of some sort..

[@wendellramcharan6365]

Is it with vectors that if you return to the starting point you have gone nowhere?

[@noahm8096]

yep! You're describing "displacement", which is indeed a vector :)

[@WillTellU]

I love vectors, they're so nice and simple and the matrix operations with them. Mmmmm.

[@ferus5583]

I wish I could understand vector analysis

[@shwetagarg1055]

Wait. Wait wait, where did 2a + 3b come from?

[@ye4us]

Why does the comprehension part sound like the drums from hotline bling?

[@SaeedNeamati]

Dave, this video is also not part of any of your special math playlists.

[@muacarine1294]

Pls sir I don't understand physics and I really want to further it pls can u help me?

[@ProfessorDaveExplains]

check out my classical physics playlist!

[@silmymuhammad2222]

this video comes under what category

[@ProfessorDaveExplains]

so most students will be introduced to vectors in algebra, and especially in introductory physics, and then when you get to advanced math like linear algebra they are all over the place

[@infinitysounds211]

Sir what's blue 🔵 shift

[@carultch]

Blue shift is an optical Doppler effect whereby an electromagnetic wave becomes higher in frequency due to the source of the wave approaching the observer. It's called a blue shift, because it shifts visible light to the blue portion of the spectrum, if it started out green at the center of the visible spectrum.

[@coffiealexankomah7646]

Pls u made a mistake in the comprehension solution

[@coronetybd]

give the example

[@danielledescuatan2806]

Its boringggg🙄🙄🙄but i still learned some thing😊😊😊

[@smitabhosale7904]

Your intro is too funny 😂😂😘

[@parcxi_1349]

bro idk what's wrong with me, I understand english very well but right now, I don't even understand anything

[@CarlDominic14]

its like Jesus teaching me school stuffs

[@mattrimol9395]

The Dave Grohl of math

[@najdatmz]

I am still beyond confused

[@hemachandran0908]

Professor Jesus

[@jeanpierremattei4073]

Merci !

[@helloyourcomputerhasvirus8832]

i wanna die

[@nikhileshsingh3531]

First

[@stummstefan9735]

my girlfriend: we have to break up.
me: what!? why?!
her: i met another guy...
me: what makes him better than me?!!!!
her: 3:13

[@danielledescuatan2806]

Its boringggg🙄🙄🙄but i still learned some thing😊😊😊