Constructing a unit normal vector to a surface | Multivariable Calculus | Khan Academy

Deriving a unit normal vector from the surface parametrization

Missed the previous lesson?

Multivariable Calculus on Khan Academy: Think calculus. Then think algebra II and working with two variables in a single equation. Now generalize and combine these two mathematical concepts, and you begin to see some of what Multivariable calculus entails, only now include multi dimensional thinking. Typical concepts or operations may include: limits and continuity, partial differentiation, multiple integration, scalar functions, and fundamental theorem of calculus in multiple dimensions.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Multivariable Calculus channel:

[alejrandom]

5:00 the most impressive part of this video is how well you drew that hand

[hr]

What a beautiful hand did you draw. Sal you are incredible

[bloodbrothers]

Omg i saw all these 199 episodes of this this is last feels good

[TheKmanOfSmash]

In his arithmetic and Pre-Algebra playlistd, Mr. Khan has tons of videos on fractions and decimals. As Khan has said and made clear before, you can literally start at 1+1 and with enough hard work and dedication end up at vector Calculus, regardless of age.

The problem is not your age or the gaps in your education. It is your resolve.

It's amazing how much humans can achieve if they dedicate themselves to something. I suggest you take advantage of that natural power.

[ivangutierrez]

Thank you so much for making these videos, they have really helped me learn, and I don't know what I would do without them.

[FinLogan]

OH MY GOSH. I thought you were just math artist but then you drew that hand. You can do anything

[Alphapox]

Thanks to your videos in Math Physics & Chemistry I can now test out of most of my introductory math classes and if (i hope) I pass my tests i can just take mostly social studies, language arts & any other hobbies in the year and a half before i have enough credits to graduate.

[BYMYSYD]

You have gotten a lot better with you're drawings Mr. Khan.

[Penger]

Hi. I was just wondering if you are going to upload any videos of complex analysis? Like complex integration, laurent series and residue problems.

[allagillarbajs]

True. In pythagoras dialogues he says:
"all humans possess all knowledge, you just have to lure it out"

[olev]

Sal could you please put next and previous video links in description, its little bit difficult to trace back to a video where current subject started. Though this might be a lot of work since you have over 3000 vids. Anyway just a suggestion.

[Ferrus]

Well this video inspired me to go read more, a surface with three parameters has a normal vector defined as the gradient of the function divided by the magnitude of that. Wonder if that will be covered later...

[hamoodhabibi]

Wow great conceptual it was so clear 👍

[Carlos-iwzm]

Instead of doing the cross product for each component, wouldn't it be simpler to apply the gradient given that the function is known?
So you'd get:
ñ(u, v)= (∆r/|∆r|)
The Delta's are suppose to be dels, idk how to type the symbol

[roro]

btw have you used coursera? if not i highly suggest it. its free

[austinjonesvelo]

I just wanted to let you know how much I like your hand

[svartiske]

I feel the same way, but if you start at the beginning, it's just like learning a new language. At least I hope so. :)

[jkjonk]

Oh the irony is so good. You're nominating him to be the nobel peace prize for teaching you and you spelled it wrong.

[cgprojectsfx]

How do you get Ru and Rv from three vectors containing (x, y, z)?

[mattismedia]

It would be awesome if you had actual examples with questions and numbers and stuff. Magnitudes easier to understand.