Calculus 3 Lecture 11.4: The Cross Product

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professor Leonard, if you wanna help the greatest number of students, you gotta start teaching teachers how to teach.

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That is a clever point of view for the problem of teachers not been able to communicate to their students. You could actually contribute by "nicely" asking the teacher to view videos on any calculus subject from Leonard.

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And use the metric system

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Wouldn’t really work most post-secondary math professor don’t have the luxury of teaching lectures over 50 mins

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Dear Professor Leonard. I don’t know if you read all the posts you get but hope you do as you deserve all the accolades you have received from students around the world. I am a 60 year old Englishman. I am not studying calculus for any courses or qualifications. But for some reason, for a long time, I’ve wanted to understand Maxwell’s equations. I did maths and physics many years ago at the University of London and I just didn’t understand any of it but was intrigued by how such complicated things regarding light and electricity and magnetism could all be related by ‘simple’ maths (in England we say ‘maths’ not ‘math’!). So here I am, working my way through it all. I was so excited when I got to proving the area of a sphere using calculus! Sad maybe, but that’s me. So, what’s the point of this ramble? Well, this shows the reach you have, the impact you have made. Learning by watching you is fun and so easy. I feel like I’m there in the classroom. I nod my head when you say “nod your head if that makes sense” and like a few others have felt so involved that I also lift my hand when I ‘get it’. You are a superstar of education. Thank you so much for what you are doing - like many of your students I wish the very best for you. And for all those students: the very best of luck - the fact that you are taking the time to make sure you achieve your goals says a lot about you all too. What a great community! Remember every day is a school day!

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Ed, I too am a self learner. I am 69 years old, and have been studying calculus off and on for the past many years, wanting to learn it well, because I didn't learn it well in college. I, too, want to understand more of physics, hence my concentration on calculus. I often turn to Professor Leonard when I do not understand what I am reading in my calculus text, because he explains the background, and gives proofs as to why the formulas work. Keep up the good work, Professor Leonard.

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Hi everybody!! Please remember, KZbin takes AWHILE before it pushes out Full1080p60pHD. Just wanted to get it out ASAP for you all. Enjoy!

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What you could do is upload the videos and schedule them to release a few hours later so that the videos have time to render and process.

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+isaac10231 Nah. I say get it out as fast as possible and if you want to wait for high res... you go ahead and wait. I'm happy enough with 360p. I can still see what he's writing on the board and get the benefit of the lecture.

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If teachers had the passion and drive like professor Leonard for Mathematics and Education as a whole. I would love to attend class everyday because I know the content will be crisp and clear. However, these days teachers lack the skill to teach which confuses the heck out of their students and "sometimes" they wonder why half of the class fails. There are too many times I'm in college lectures, and I wonder what in the world did I just learn or that didn't make any sense with a look of confusion all over my face! Thank you Professor Leonard for being such a good role model!

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Note to self: Ex: 27:05 Find two vectors orthogonal to both *v* and *w* Ex: 39:05 Find two unit vectors orthogonal to both *v* and *w* Ex: 1:12:20 Find the area of a triangle Ex: 1:40:10 Find the volume of a parallelepiped

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Professor Leonard, what a teacher! His enthusiasm for the subject , punctuated with wit, is infectious. There are those that know, and much rarer those that can teach what they know, professor Leonard is a rare breed. I only hope all who watch these videos really appreciate what they are getting for free. Thank you for re-kindling my interest in mathematics. Sir , the world is a much richer place while you are here and I hope you achieve all the success you deserve .

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I learned more from 20 minutes of this video than a week's worth of lectures.

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@@SteamPunkLV Check out the book "University Physics With Modern Physics", that's a great book that starts from the beginning (vectors, displacements, forces etc) and only expects some basic understanding in differential and integral calculus.

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Professor Leonard ,thank you for another well explained video/lecture on The Cross Product in Calculus Three. This material always helps students in different fields of study. These topics are a huge part of Linear Algebra/Statics.

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Besides the obvious teaching finesse and thoroughness, the great thing about these videos is that he doesn't have a camera operator. The camera locked-down and framed on the board is the only way to film lectures. I can't count the number of lecture videos I have seen in which the camera is panning and zooming all over the place, and making it nearly impossible to read and assimilate the information on the board. The exception is with lectures like MIT Prof. Lewin's Physics lectures in which he performs live experiments and uses a very long chalk board. So thanks for keeping it simple and allowing us to see the information.

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I would accept that explanation.

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Looking forward to Lecture 16. I can just imagine how excited this guy would get about e.

[@taekwondotime]

@1:37:00 FYI: This is also referred to as a *"scalar triple product"* and is sometimes notated like this: *(a b c)*

[@shrey9660]

[a b c] **

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respect for your teaching style. makes me excited to learn about the topic at hand.

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Greatest Professor ever!

[@Peter_1986]

If you have 2 vectors called *a* and *b,* then you can derive the components for an orthogonal vector *c* by calculating *a⋅c* = 0 and *b⋅c* = 0, and then writing all components in terms of one of those components (like c₃ = c₃, for example). Then you can set that component to a value that removes all the denominators.

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Savior of the semester!!

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Every zoom have this quality of teaching

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who need to study at university nowadays, you have all you need at youtube often better than your university lecturs =)

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best professor

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Pranaam gurudeva 🌹🌹🌹🌹🌹🙏🙏🙏🙏🙏

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You are awesome professor Leonard

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I’m so sad that my “teacher” doesn’t even prove anything and just gives the formulas..... the way u explained it .... wow.... u r a TEACHER🤩 I appreciate u (Unlike your students in this video😂 they’ll thank u someday)

[@sufiyansadiq9962]

u and v are 2 vectors and there cross product is 0, then it could also mean that either u = 0 or v = 0 or they might be parallel. Thus it might also be possible for 2 vectors to have a cross product to be 0 and a dot product to be 0 as well if either u = 0 or v = 0

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please make a video explaining your gym routine ASAP

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this guy is a hero

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HE BLESSED HIM AT 11:15!

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You have inspired me to become a professor

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Leonard, you are an amazing teacher. And also handsome!

[@alexalex-wl3bh]

Very simple presentation with all Vector's explanation.... Guyz just look this --------------- kzbin.info/www/bejne/kJqtn2Svra11gJo

[@1973jdmc]

Thank you once again for great tutorial and for being such a brilliant teacher-

[@Peter_1986]

The Cross Product might be more convenient for parallelity checks of two vectors A and B if you are using a math program like MatLab or something, since this allows you to simply check the solution for "cross(A,B)".

[@AnhTran-ff5co]

you are really good teacher. I love your lectures very much ! You are my angle ^^

[@smelly_code_odor_coder]

(0:00:00) Determinant/Cross Product (0:02:05) Determinant of 3x3 Matrices

[@AAKFKEK315]

Thank you for this great content

[@radwizard]

@16:25 you can distribute the negative instead of factoring it out. Might be easier for you to see it that way. Do it on paper and you will see. After all, math is not a spectator sport.

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You are unbelievable teacher!! God bless you🌹 and wish you all the best in your life💐♥ Lots of love*😍😘😘Mike...

[@anjaleenarain979]

Thank You professor.

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Thnaks for explaining it so well!

[@RamirezA1422]

52:52 "That's cool, that's pretty cool. Now if you dont see the coolness yet, don't worry it's gonna get chilly"

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nice teaching

[@sssmith41]

Professor Leonard -- You should take some time to start teaching teachers how to teach because the world needs that and you're the chosen one! Know it might be a little burdensome but don't deprive the world of you and teaching teachers how to teach!

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Nobody: Professor Leonard: Wanna know something that's kinda cool?

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ده س خؤش

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I liked this lecture, thank you.

[@APresidentsRansom]

Hey Professor Leonard, I had a question. You mentioned Calc IV and Differential Equations in this video, and said you did Calc III and DE. I know they are generally the same, but do you have a playlist or videos of you covering the DE curriculum? Or are they incorporated at the end of your Calc III playlist? That would be great if I could learn DE from you too! Thanks!

[@restitutororbis964]

No, he is barely about to film the DE videos, he is posting the first lecture either today or tomorrow.

[@AnthonyGosal1452]

Love the videos. Keep up the good work!

[@AnhTran-ff5co]

Thank you verymuch !!! thumbs up for you, professsor !

[@danielolivera2618]

the worst is when you are taking calc 3 in summer and your teacher SUCKS!!!!!!! thank you so much mr. leonard. when im done with all my math i will take you out for lunch.

[@ke6757]

me too man.. me too :'(

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This is soooo good