Position vector valued functions | Multivariable Calculus | Khan Academy

[@billymcgregor2067]

Wait a minute that's not grant's voice

[@chao.j]

set playback speed to 1.25 x, it starts to sound like grant :-)

[@That_One_Guy...]

@@chao.j it's only you who think of that

[@armstrongtixid6873]

That's Sal's. Sal took over for a bit, but Grant did most of the work ;)

[@donwald3436]

Grant took too much testosterone that day.

[@mukarrammallick7546]

@@donwald3436 NAILED IT. XD

[@y.a.46]

I feel betrayed. Comeback Grant. His enthusiasm really made it easier to understand.

[@theovisbecq33]

Does Grant come back in future videos of the serie ?

[@MayankGoel447]

Yup just 2 videos later

[@andrewdavies5722]

graaaaaant!!! come back.... nooooooo!!!

[@souvikroy6237]

😂 i can understand your feelings

[@Mathieu-qx7bp]

Well... I prefer Grant's voice, but you gotta admit Sal's writing is way better here x)

[@kamalb]

Sal?

[@iwtwb8]

The transition is jarring.

[@bhavna6565]

Kamal Banga nooooo man i need grant back on this one

[@nickmilkshake2661]

Agreed

[@iekenta03]

Awesome dude. You have no idea how many people you help out with this :).

[@micahdelaurentis6551]

what work have we been doing with line integrals?

[@carultch]

Probably in a previous video, he gave other examples of how to do line integrals.
An application of line integrals, is physical work. If the vector field represents a force field, then a line integral along a space curve will give you the work done by that force field, as an object takes that path.

[@jaakkokuu]

Once again. you make this so easy to understand.

[@dreia2405]

You are a great teacher, thank you

[@elvinespino5957]

Thanks, man! The transcription at the bottom helped a lot

[@michaelhernandez2724]

The vector-valued function generates each of the terminal point of the position vectors evaluated at t- value specifying a point on the plane curve.

[@tielessin]

No panic! It's just 4 videos that'll prepare you for the coming multi variable calculus concepts that Grant will teach you after that.

[@bat102]

at the beginning of the video "line integral " is mentioned which hasn't been covered in the videos prior to this in the playlist, is it due to a mistake in the items' order?

[@ihibthegreat5343]

its same way on the actual sight. Probably an artifact from before Grant from 3blue1brown did the first part.

[@sams6454]

if you watch it on khanacademy.com it is fixed and edited out.

[@smolytchannel5062]

This video is 6 years before the previous one. So yeah maybe

[@nevilholmes5900]

Thanks

[@scholar-mj3om]

Marvellous💯

[@yichizhang795]

Awesome!

[@esmondlucan4269]

GEOMETRIC FORMS CAN BE REDUCED. TO LOGARITHMIC. FORMS WHICH CAN BE FURTHER REDUCED TO ALGEBRAIC FORMS

[@emmanuellagalley7914]

I love it😍🤭

[@johnr1875]

does it matter that the curve, C, is not a function? is it because its parameterized?

[@SidIndian082]

Finally sir is back 🙏🙏🙏❤️❤️❤️😍😍😍

[@v7e4n8om]

Vector Equation of a line!!!! pls

[@hermonokhidievbie6593]

ikrr

[@That_One_Guy...]

Check linear algebra playlist

[@samuelleizerman5832]

***** click on the cc logo that says captions when you mouseover it, then click off.

[@oneinabillion654]

*SAL APPEARS*

[@sw1285-q5o]

scalrrrrrr, vectrrrrrrrrrrrrrrr🙃

[@halogenhali583]

Greaaaat

[@tomaslopez814]

Grantdaddy?

[@agrimsingh001]

sal is back

[@kaustubhpandey1395]

Hello Sal, where was Grant?
Edit: Oh this was years prior

[@BareClause]

me not happy atm lolz

[@Raikaska]

I thought the curve was "C", not "S"

[@HabiburRahman-xs9gb]

in simple language, position vectors must have an starting point which is (0,0)...right?

[@Suarsaa69]

Somehow I am able to understand Sal's videos even at 1.75x, but not grant's 8(

[@Sheeeeshack]

Sal kidnapped Grant or sth?

[@ThickDonut-ln1ub]

No Grant kidnapped Sal to make him do the work for Grant lol

[@matthewwroblewski8752]

Kewlio dadio