1.1 Length of a 3-Dimensional Vector

www.rootmath.org | Linear Algebra
In this video we'll derive a formula for finding the length of a 3-dimensional vector. We'll also briefly discuss how to find the length of a vector with more than 3 components.

[@manasitripathy7113]

My teacher just game me the formulae without any explanation. I was in doubt until I found you. Thanks a lot! You are the best!

[@fadhil4008]

Yeah, my teacher either. This chanel helps me a lot about a vektor explanation

[@OkCoffeeIsNice]

Wow so informative! I couldn’t believe that plot twist when the length of the vector was just all the components squared and the square root of that.

[@The_Engineer]

9 year later and i still appreciate ur amazing videos

[@rootmath]

9 years later and I still appreciate comments like this, thanks for watching!

[@ScorpiaX]

thanks for the easy-to-read concise videos. I'm glad that someone spent their time putting up the supplementary lessons. If only there were more sets of these videos I could watch.

[@Amit--yadav_26110]

This video is 12 years old. I appreciate your hard work.....

[@runiyobeen12]

Thanks alot now length of 3D vector formula makes a sense

[@hmbunn2014]

This explanation was so much easier to understand, thank you!!

[@PhysicsOfParkour]

Thanks a lot I paused the Vid and found the Ans before it was revealed. Nice Tutorial; keep up the work!

[@danielketcheson1965]

You know you've found your teacher when RUclips loads a video different from the supposed subsequent one you were going to watch, you say hard pass, go to the guys channel and make a playlist.

[@TheFreakyVibes]

this proof was so beautiful I think cried a little

[@buanasetra7031]

this video really helped me, thankyou

[@DimitrRaev]

Great tutorial, can someo ne tell me what is the program he useses for drawing ?

[@RahellOmer]

God bless you! You are better than my math teacher! =D

[@SlashU631]

woooo, THANKS a lot, now I can finish making my mmo radar application.

[@Rookblunder]

Wanted to verify about using a third component when rooting and you showed the proof. Thank a lot.

[@nandinisingha3357]

That's the best I got in the whole RUclips

[@_art9267]

sooo clear, THANK YOU!

[@frostbird3431]

Could you tell me what the program used for drawing is?

[@rootmath]

I use Gimp for all the drawing

[@joyrahman7516]

Really making it look simple. Do you have a website?

[@danieldoradotoro334]

What software do you use for drawing?

[@paulrulez742]

Did you ever find an answer to this? I feel as if messing around on this could help visualizing the resultant vectors a bit easier.

[@Diamond_Hanz]

2020 here... this guy is GOAT

[@chaiyihein]

love you, brilliant xplanation

[@tshepangmukama7078]

finally this thing makes sense,thanks to you

[@thabsor]

thanks man, I couldn't grasp why the formula was that

[@J.A.G790]

My god THAT is a great explanation thank you

[@12thando34]

thaks for the videos man you really helpinn people out and god bless

[@AgFan176]

Wow, this made so much more sense. Thank you!!

[@ranulmbalasooriya659]

Thank you so much

[@samehsaad4200]

Which program u use for writing and recording

[@susanchack4983]

Thank you sir, this has helped me very much.

[@nipunyadav989]

THANK YOU SO SO SO MUCH!!!!!!!!

[@ymazalmazal1757]

very nice thank you much for sharing... So clear !!!

[@sigmasandtutorsptyltd4420]

Hi rootmath. I have a problem with "b". Is "b" in the first example really the hypotenuse of the second triangle? It looks like the opposite side to me.

[@ankitaaarya]

Yea it happened with me too, but trust me it really is hypotenuse. I thought it was adjacent but I was wrong.

[@ankitaaarya]

But the real question I couldn't get my head around is that, how do you graph vectors with 4 components.

[@STKeTcH]

what if it has variables , for instance what is the length of ?

[@yashtiwari6702]

What if the vector is in 2 dimmension will we use the root of the sum of the square of all sides of a triangle?

[@abhiraj777]

Thanks you saved me :)

[@KM-nx5sh]

beautiful

[@manojghosh5108]

GOD LEVEL!!!!!!!! EXPLANATION

[@H3aDsH0tGuy1]

Why is the second one not a right triangle?

[@idude001]

Hi there, does it matter whether the vector is a row vector (u') or does it have to be vertical? Thanks

[@dasdarklord2363]

It doesnt matter

[@ianjaydelosangeles3173]

what is the 4th dimension?

[@fadhil4008]

Yeah i got confused too, why did 7:00 have 4 components? Even more 6 components :/

[@echo.1209]

@@fadhil4008 I know this is three years old now, but vectors are a way of representing numbers that can be de-attached from space. So, you don't need to be able to visualise a fourth dimension to write a vector with four components. In fact, a lot of math involves vectors or matrices with more dimensions than we have in our real world. It may be hard to understand, but vectors are an abstract concept. While two-dimensional or three-dimensional vectors can be drawn on a graph or in three-dimensional space, you can't rely on visualisations to fully grasp vectors at a higher level.

[@titaatomsa]

How represent three deimesion

[@SweetShine213]

Thank you!

[@jugobugo]

thanks a lot

[@thabsor]

thanks man

[@shoutotodoroki]

Best best bessssst!!!

[@Safwan.Hossain]

Yeah good vid. Just using the formula, which is pretty simple tbh, isn't very useful without understanding it especially once u get to more complex questions.

[@fitwithartin]

Awesome

[@sudekara6387]

Thank you....

[@otsutsukiboruto8833]

v =
−1
2
5
3
Then: ||v|| = 1 + 4 + 25 + 9 = sqrt(39)
𝑤 = −6 ∙ v
Results: 𝑤 = 6 *sqrt(39)
My Teacher did this after he came up with the sqrt (39)
does anyone know why ? and what is this (6) excatly?
Thanks in advance

[@rootmath]

||w|| = ||-6v|| = ||-6||*||v|| = 6sqrt(39)
The third equality is a property, the length acts alot like an absolute value but the intuition is, if you multiple a vector by 6 it will be 6 times longer

[@sSUPERHITZZ]

fabulous

[@woredding]

and why would a vector have 4 components? in a 4d world?

[@jean-marctrappier4436]

String Theory talks about more than 11 dimensions (with time dimension) so 4 dimensions isn't that impossible, just our own reality already got 4 since you can add time to the 3 you obvioulsy already know.

[@tjeerd2176]

Wow its just that easy

[@geemithafernando]

Wow.ur awesome

[@NickGhale]

Thx m9

[@tamizhazhagan-jaishreekris2199]

Damn cute 👌 😘

[@dogwithwigwamz.7320]

WTF is this crap ? The root of (1 squared + 4 squared + 3 squared ) is the root of 26. Or is it the case of `why make things that are easy difficult ? `