Calculus 3 Lecture 11.4: The Cross Product
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- Опубликовано: 8 сен 2024
- Calculus 3 Lecture 11.4: The Cross Product: Finding the Cross Product of two vectors with Determinants, Using the Cross Product to find Mutually Orthogonal Vectors (with proofs), Torque, Area of a Parallelogram, Volume of a Parallelepiped, and Coplanar Vectors.
Hi everybody!! Please remember, RUclips takes AWHILE before it pushes
out Full1080p60pHD. Just wanted to get it out ASAP for you all. Enjoy!
Thank you soooo much😍😘i really wish that you were my teacher... I love u sooo soo so much please Can you tell me what's your horoscope sign?? Please answer me if you can🌹
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.
+Professor Leonard Do you publish these as you go, or are these from the fall semester? Just curious how you're pumping out what seems to be a week and a half of lectures this quickly.
+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.
Well good video i was playing video games and forgot to study so i watched this it helped out ALOT.
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!
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.
@@davidestabrook954 You too! That's honorable work you are doing.
Same here. Learning math(s) just for fun, and having a blast doing it through Prof. Leonard and Khan Academy. One year ago my level was pre-algebra. Today I am having fun in Calc III. Next year I shall understand the equations of general relativity. Every day is a school day!
67 and a long-time programmer. Stopped at calc 1 many moons ago and now working my way though all the math needed to participate in the AI revolution. Your courses have been the core of my math education over the past 6 months and I can't thank you enough. There are other teachers of merit -- Khan certainly comes to mind, but none that I can listen to for long periods of time without wanting to jump out of my skin, haha. I guess I'm not a born lover of math, but just sharp enough to understand enough to keep moving forward in my quest.
Sir, I am a 24-year-old self learner who learns maths "for the sake of God" in my words. With a one single comment of yours, you have become an inspiration to me. May God give you a long, healthy life full of mathematical learning. This world is lucky to have people like you.
seriously these kids dont appreciate this prof leonard enough hahah he's got jokes!
professor Leonard, if you wanna help the greatest number of students, you gotta start teaching teachers how to teach.
+ghalib khan
"Ghalib film dekhi hai aap ne" ?
What a great and true comment! Professor Leonard -- you need to take some time to start teaching teachers how to teach because the world needs that and you're the chosen one!
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.
And use the metric system
Wouldn’t really work most post-secondary math professor don’t have the luxury of teaching lectures over 50 mins
This is the most ripped math teacher I have ever seen.
He's a cross product of intellect and manliness.
Ive had a cross product of this man and physics for my engineering teacher in high-school, love the lectures!
that doesn't mean what you think it means lol@@elisasumber6476
😂😂😅
One of the best ones
Whenever you finish a 2+ hr lecture of Professor Leonard's with accompanying pages of notes taken, at the end you feel like you're emerging from the mathematical cave of knowledge back into the real world, with a boatload of new knowledge and understanding.
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!
Well, if your teachers aren't producing, you can always come here. God bless the internet.
I was just zoned out when he said "Come on, stay with me here.". Wow.
😂😂😂
It happened to me the dot product video 😂😂😂
What are you studying
Chemical Engineering major here. This guy has made math fun again. A friend recommended me to watch your videos and I'm so glad I decided to check them out. I'm taking Calc3 now and planning to take differential equations over the winter term. At first I had hesitations, but I know I'll be fine now, given how amazing of a teacher you've been thus far. Thank you so much for making these free to view. Most students already shell out an arm an a leg for a shit teacher. It's nice to know there are resources (like you) when the $4,000 tuition just doesn't cut it on quality education.
I trust the Leonard. He's gotten me this far!
We need more Leonards at universities around the world.
Very simple presentation with all Vector's explanation.... Guyz just look this --------------- ruclips.net/video/ZiJn1yxHBJ8/видео.html
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
These comments are great when I want to supplement Leonard's lectures with my professor's, thanks!
Professor Leonard you are such a lifesaver, I have been struggling through my online calc 3 class for the past few weeks now and your videos have been so so so helpful, thank you so much for providing this resource.
I wanna be like him, intelligent and buff.
Although I already know what he's teaching. it's just so fun to watch him teach. plus I learn some things that weren't clearly explained in my classes. #bestteacherever
Taking Calc 3 this semester, thanks for the help!
Beyond grateful that you have kept all the calc videos on your channel after 3 years. They are saving me right now, my professor went through the dot product, cross product and three dimensional coordinate system in one two hour class. I was so lost trying to do the hw. But these lectures are gold! Thank you so much!!!
I may owe my degree to you someday :) Thank you so much for these videos! I wish my instructors made calculus this easy to understand. You are a lifesaver!
Hey,
Did you graduate ???
what a fab. professor ,u are really superman for us .
You should teach Physics!
A dream come true. Sadly, he revealed in one of his lectures that his Physics teacher was really bad, which is why he never really understood it :(. But he's an awesome math teacher!
Your passion to teach makes big difference on your followers. Keep up pro. Leonard
@@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.
I watched all the Calculus 2 videos and learned a lot, I am 𝐯𝐞𝐫𝐲 𝐠𝐫𝐚𝐭𝐞𝐟𝐮𝐥 for this work, it helps me and thousands of other students succeed in Mathematics. Currently I take Calculus 3, I understood the first 3 lectures, but this one starts with Matrices. I wonder whether you have a separate lecture explaining Matrix, I couldn't find it in the playlists.
Leonard, You are going to be in the $$$ if you keep this up. Many Thanks. Still beat any other open course ware I have seen when it comes to math education.
Saved me for mid-terms and now saving me for finals! THANK YOU!:D
I swear that Prof only does these lectures to show his *magnificent and bursting arms*.
I don't know, I smell a conspiracy here.
I'm a heterosexual man and you don't hear me complaining.
I would accept that explanation.
Now I understand why he keeps mentioning his wife throughout his videos...
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 .
Huh! He is so wonderful..God bless u
@1:37:00 FYI: This is also referred to as a *"scalar triple product"* and is sometimes notated like this:
*(a b c)*
[a b c] **
Amazing professor!!! Thank you so much for uploading your lectures. They are very easy to follow and your passion shines through them!
Hi what are you studying
Hi what are you studying
\
@@user-zr2cs5zg6q
Thank you thank you thank you!!!!!! I can't say enough thank you for being such an awesome teacher professor Leonard. You are the only reason I'm surviving right now.
Damn I struggled so much with torque in my physics class, in two minutes you have explained it perfectly by swinging those massive arms around. Best teacher out there seriously! Many thanks
Very simple presentation with all Vector's explanation.... Guyz just look this --------------- ruclips.net/video/ZiJn1yxHBJ8/видео.html
I learned more from 20 minutes of this video than a week's worth of lectures.
Professor Leonard are a legend of our times. I will tell stories to my grandchildren about the Professor of RUclips that got me through my classes with mediocre teachers! I've gotten to this point in math thanks to you, as I'm sure many other students have! Thanks for making math entertaining. Professor Leonord for President 2020!
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.
THANK YOU SO MUCH UGH I WISH I WAS TAUGHT THIS WAY THE FIRST TIME
Very simple presentation with all Vector's explanation.... Guyz just look this --------------- ruclips.net/video/ZiJn1yxHBJ8/видео.html
Just want to say thank you Professor Leonard for posting these high quality lectures. Mondays and Wednesdays I have my regular Multivar and Vector Calc professor. The rest of the week, I'm taking your class. Thanks for all the help!
Dear professor Leonard, thank you so much for sharing these videos. They are very helpful for me to learn calc 3. I really appreciate that you explain the ideas behind the theories (instead of just giving us all the formulas and plug in the values) and make all of them so clear!
Blessed be the day that this man decided to publish his lectures on youtube.
This prof loves his work/subject so much it makes me want to listen.
Thank you so much! I have been waiting for these videos and they literally saved me for midterms! You are the best!!
Thank you so much Professor Leonard! NOW I have hope to pass this class :)
Professor Leonard makes understanding vectors so easy for those who do not intuitively understand them. Professors need to take note of how he explains concepts and how he teaches them.
I struggled to understand these last two topics in my calculus and I came to youtube as a last-ditch effort before my exam. Thank you so much!
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"
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.
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.
I love these videos. Your videos on statistics have helped me tremendously. I have gotten 100% weeks every week. THANK YOU SO MUCH!!!!
you are the best professor ever... and you teach way better than my teacher. i love all your vids from calculus 1❤❣
1:39:55 Professor Leonard I trust you more then I trust anyone. And you have earned every ounce of it.
Every time I watch another video and look at the subscribe count, I see the number go up another few thousand. I hope the streak keeps going.
You made this chapter so easy to understand Professor Leonard, good job!
Professor Leonard is The Best👌👌👍
@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.
thanks for all the help! you're an amazing professor. hugs from brazil - federal university of rio grande do sul
respect for your teaching style. makes me excited to learn about the topic at hand.
Savior of the semester!!
oh boy i just finished 2 semesters of physics and now i am taking calc 3. I really wish I watched these videos before taking physics, it would have helped tremendously.
You are relay a professor born to teach .....................Thanks.
I just studies for our first Calc 3 Test from these Videos, Thank You Very Much!! Wish you taught at our College.
you helpd me to score all my calculus courceA+ thank you very much I am from Ethiopia
Professor Leonard, Thank you so much all of these video tutorials.
1:01:01 when he gets so excited he drops the pen flailing his arms to visualize the vectors lol love it
Same haha
Looking forward to Lecture 16. I can just imagine how excited this guy would get about e.
thank you very much , Professor Leonard.
This is the best lecture on calculus 3
best professor
Greatest Professor ever!
got to love the refreshers of calculus
He just love to make every thing make since, I love that
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)".
Thnaks for explaining it so well!
I am dying to see Prof Leonard do an online live class! That would be so amazing!
HE BLESSED HIM AT 11:15!
Thank you once again for great tutorial and for being such a brilliant teacher-
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
Amazing work. Far better than my prof!!! Thank you so much!
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.
me too man.. me too :'(
Nobody:
Professor Leonard: Wanna know something that's kinda cool?
Amazing//// amazing. it was very very good..... 10x a lot.
1:37:07 spat out my coffee all over my computer screen
drink water every time he says "vector"
you are really good teacher. I love your lectures very much ! You are my angle ^^
You are awesome professor Leonard
May The Loving Creator bless you for your effort.
please make a video explaining your gym routine ASAP
I love this man
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)
You are unbelievable teacher!! God bless you🌹 and wish you all the best in your life💐♥ Lots of love*😍😘😘Mike...
Love the videos. Keep up the good work!
(0:00:00) Determinant/Cross Product
(0:02:05) Determinant of 3x3 Matrices
Thank you verymuch !!! thumbs up for you, professsor !
Follow the Leonard's advice about life! He has literally helped hundreds of thousands of students learn and appreciate calculus!
Thank you for this great content
at 1:15:52 when the guy says "dot product" prof leonard does a face for a moment that kinda reminds me of homelander lmao
Leonard, you are an amazing teacher. And also handsome!
Very simple presentation with all Vector's explanation.... Guyz just look this --------------- ruclips.net/video/ZiJn1yxHBJ8/видео.html
I'm trying to learn but I keep finding myself distracted by those twin "120mm cannons."
52:27 i jumped out of my chair and closed my notebook. I was done with math for the day.
Every zoom have this quality of teaching
Thank You professor.
this guy is a hero
Pranaam gurudeva 🌹🌹🌹🌹🌹🙏🙏🙏🙏🙏
who need to study at university nowadays, you have all you need at youtube often better than your university lecturs =)